Ever since Tolkien most, if not all, works of fiction including orcs portray them with tusks. Though this achieves the effect of portraying them as animalistic, what would the real world applications of this feature be? Would it cause any health problems or change their dietary preferences?
It Reflects Dietary Differences and Requires Surprisingly Little Hand-Waving
The answer is going to depend on whether the tusks grow up out of the lower jaw, down out of the upper jaw, or in some other direction. Each will have starkly different uses, benefits, and detracting aspects. For the sake of brevity and because they are the most common depictions, I will only consider tusks that grow from the lower jaw up, as in this fellow:
The short story of this post is that it's probably not better or worse, just different. Well, maybe a bit worse, but it's not a show-stopper.
Here's the big issue with small tusks that grow upwards - they aren't terribly useful for a tool-using species.
They can absolutely be used to help tear meat from a carcass that has already been felled, but you would have to really shove your face right in there to do it. For a species that has tool-use capability (they probably used tools to bring down the prey, actually), it doesn't make sense that they would then shove their faces in to strip the meat off.
There are other animals that have tusks that grow upwards - boars and hippos come to mind - but they largely use that set for face-on-face aggression. Given the comparably small size of typical orc tusks and the fact that they can use fists and weapons, the need for face-on-face aggression is minimal at best, and most likely non-existent.
These issues can probably be hand-waved by suggesting that previously the physiology of orcs suggested that they did participate in face-on-face fighting, back before they were walking fully upright and using tools. Back then their tusks were larger, and have been shrinking over thousands of years. They could be used more for decoration and intimidation (as in the picture above) than for other purposes.
Dental Structure and Resulting Diet
I'm sure dentists all over the world cringe at Orcs, and not because of their brutish behavior and strength. They are so often depicted as having tusks that are next to human-looking teeth, and that's just ridiculous. Human-like teeth are prone to crowding problems, which create alignment issues, which jacks with the whole musculature of your face - and that's without trying to make room for the growth of very large teeth.
What you would actually end up with is something more akin to the sabertooth tiger (albeit upside-down), where there is actually a good gap near the tusks and on the opposite side of the jaw:
This is going to create a situation where, like the sabertooth tiger, the Orc is necessarily largely (if not entirely) carnivorous. Unlike in a hippo or warthog, I would guess that the jaw structure leaves too little space for grinding teeth for plant matter to be a substantial part of the diet. That does jive with many descriptions of Orcs though, and there are many instances of carnivorous animals out there that demonstrate it is a successful survival strategy (though I am not convinced it could give rise to a sentient, social species).
Jaw-attached tusks have many of the same problems as teeth, though to greater and lesser degrees. For example, while cavities (or cavity-like issues) are still a problem, it would be less a problem for orcs than for people. This is because cavities are often caused by a buildup of acid between teeth, but tusks require the existence of space between the tusk and other teeth, which reduces the occurrence and impact.
Issues that would be higher though include the fact that, being larger and external to the face, they would be more likely to be knocked/impacted and chip/break.
They would also force the owners mouth open somewhat, which introduces a vector for pathogens. However, it is likely that orcs have other adaptations to assist with that issue, particularly because they are also likely carnivorous and used to eating raw meat.
This is probably the area where most depictions get things wrong. Usually we see orcs as humans with some big teeth, but it doesn't just work that way. To support the added weight and distribution, the entire complex of muscles that works the jaw would need to be re-worked, which would impact neck, shoulder, and back musculature as well. The most noticeable difference would probably be that their face would tend to bulge more where the jaw attaches. It would probably move them closer to the uncanny valley and make them even more repulsive to humans.
While there might have been a strictly practical use for these teeth earlier in their evolution--look to @GrinningX's answer for that, it had to have been selected for long after they have a use for it.
After all, if they have hands and tools, they would not need them very much.
I am going to draw a parallel between orc tusks and human breasts here.
Humans are strange when it comes to mammary glands. Bigger breasted women have been selected for, and thus, most ladies have mounds in that area. They've been selected as a positive sexual characteristic. But honestly, in the form they come, they are certainly not practical. While mammals and primates have boobs, they certainly aren't at all like human breasts. So...why? They don't make running very easy, and the larger size doesn't make for more efficient sources of milk for young.
The answer is as far as we can guess, is that collectively, males of the species found this more attractive, so we selected for breasts. More bosoms equaled more of a chance to reproduce, and was seen as an indicator of fitness and attractiveness.
So your tusks can be the same kind of thing. If you want them more prominent on males, tie it to testosterone levels--making it like deer antlers (while they fight with them, they are also for display). Females have antlers, but not as prominently as males.
So orcs aren't always that smart in fantasy lit. And there may actually be a little bit a of a biological reason for that. Jaw strength.
See, in humans, we were able to develop a bigger brain later in our development because we lost muscle strength, in particular, in the jaw. There's a theory that a genetic mutation which governs jaw strength, which weakened in proto-humans, was a trade off for better intelligence. It's more complex than that, actually (see the quote below), but there might be at least a little bit of a trade-off--stronger, and more muscular equals less brain power for the species over-all.
our jaw muscles need to exert considerably less force from to produce it. This explains some peculiar characteristics of our skulls. Our teeth are as tough as those of other primates because they still need to withstand the relatively high forces exerted by our bite. But the rest of our skull can afford to be comparatively flimsier. The jaw muscles attach to the skull and inflict stress upon it when they work. But our jaw muscles can produce a strong bite through less effort than those of other primates. As such, they inflict fewer stresses upon the skull, which can afford to abandon some of its sturdiness. SOURCE
As for medical problems, may I invite you to Tusk/Dental Care for Pigs!
I know you are thrilled beyond measure by this introduction.
At about 5 to 7 months of age, the permanent canine teeth will erupt. These canine teeth grow continuously throughout the pig's life. They should be first trimmed at about 1 year of age and then trimmed on an annual basis. Without trimming, the canine teeth will become elongated and cause discomfort and a misaligned bite.
You could have teeth and/or tusks work this way, so they actually have to file them and maintain them regularly.
Could be anything really. Take a look at this list of tusked animals. You've got walruses, elephants, hippos, pigs--notice that some of these are actually... ::gasp:: vegetarians.
Here's what the wild boar eats:
The Wild Boar is an omnivorous animal that primarily feeds on plants. Plant matter comprises around 90% of the Wild Boar's diet as they feed on young leaves, berries, grasses and fruits, and unearth roots and bulbs from the ground with their hard snouts. Living in highly seasonal regions, Wild Boars have had to adapt to the changing fruits and flowers, and are known to favour the protein-rich nuts (such as acorns) that become available in the autumn and prepare them for the winter ahead. They will however, eat almost anything that will fit into their mouths, and supplement their diet by eating eggs, Mice, Lizards, Worms and even Snakes. Wild Boar will also happily finish off the abandoned kill of another animal. SOURCE
Mostly plants, but pretty much anything they can get their hands on.
I'd say that orcs are more likely to be equal opportunity eaters. That is, omnivorous, so they can eat anything. It would be kind of fun to make most of them vegetarians.
Tusks are terribly effective weapons when fighting close range. Look at wild boars: they use their tusks while charging the enemy
boar typically attacks by charging and pointing its tusks towards the intended victim, with most injuries occurring on the thigh region. Once the initial attack is over, the boar steps back, takes position and attacks again if the victim is still moving, only ending once the victim is completely incapacitated
If they hit it's not going to be funny.
Re "Ever since Tolkien...", were there orcs - using that name, not just orc-like creatures - in literature prior to Tolkien?
Now perhaps my memory is failing, but I don't recall Tolkien describing orcs as having tusks. Fangs, perhaps, such as apes have - which pretty much answers both facets of the question, doesn't it? Orcs have fangs (and their other qualities) because they are rather ape-like. And we can get an idea of their diet & behaviour by looking at what real-world apes do with their fangs.
AFAIK that's a remnant because they evolved from boars instead of apes, also the shape of their nose match.
"Modern" usage of the feature is (probably) to dig into your chest to eat your heart (NOTE: real boar tusks are used to dig into the ground to unearth edible roots and insects, beside males fighting in the mating season).
Their application may be for display. Bigger tusks could reflect a more fit individual and give them an advantage in attracting a mate (do orcs mate, I know in the Tolkien world all sentient species were created so the biology is beyond me)
They could also be able to be a display of social dominance (we don't have to fight because you are so much more tusky than me and I know I will lose).
As for problems, all sorts of heath problems could be caused by having a massive lower jaw to support tusks or difficulty eating, or real problems of an ingrown tusk pointing the wrong way.
It could be an "accident" of evolution. Primitive, pre-tool orcs used in the same way that boars do: they possibly had powerful jaws that could open wide and used them as the primary weapon. They might have become genetically linked (if such a thing is possible!) with the general health of the orc, and as such they become a symbol of sexual attractiveness.
Most importantly, they must never have become a hindrance to the orc's survival.
Then, by the time they learned to use tools and weapons, they were well established and they never lost them.
From Wikipedia: https://en.wikipedia.org/wiki/Orc
"In The Silmarillion, Tolkien conceived the Orcs to be Elves who had been enslaved and tortured by Morgoth and broken and twisted into his evil soldiers. In other versions of their origin, including those from Tolkien's notes, the Orcs are depicted as the parodies or false-creations of Morgoth, animated solely by his evil will or perhaps, by his own diffused essence, and made intentionally to mock or spite Eru Ilúvatar's creations—the Eldar and Edain."
Like other posters have said, orcs had fangs. There was no evolutionary or practical reason for them to have fangs, much less big tusks. Their bodies were they way they were because Morgoth hated the other Valar (gods) and he deliberately made the orcs evil and horrible in body and mind to mock the creation of Elves and Men.
I remember from The Silmarillion that Morgoth was angry that other gods created children but the supreme god put a stop to it before Morgoth could create a race of children, which is why he twisted Men and Elves. I think he also created the dragons, trolls, balrogs, and most of the other evil creatures. Shelob the Spider was a notable exception, being a daughter of Ungoliant, a primordial spider demon.
Morgoth was a god, and he had godlike powers strong enough to corrupt spirits, raise mountains and warp life. Sauron was one of Morgoth's original corrupted spirits, which shows you how powerful Morgoth was.
Dungeons & Dragons (1977) depicted orcs as pig-like creatures with tusks on their lower jaws. Tolkien orcs were never like that.
If the orcs you're thinking of are natural creatures, they might have tusks left over from an earlier stage of evolution. Perhaps they evolved from baboons, who have very dangerous fangs.
Like another poster mentioned, tusks on the lower jaw could be for digging or even ripping up tree bark to get at insects beneath. Once prey was dead, an orc could use his tusks to rip open the carcass to get at the raw meat. I don't think they'd be that good for attacking because they'd depend on the strength of his jaw muscles alone instead of being driven by the strength of his neck, shoulders and core like immobile upper jaw fangs.
For health problems, big tusks would interfere with an orc's ability to fully close his lips. He would get tooth damage from dry mouth, probably have a problem with saliva irritating his lips and chin, and slurring his words. Breaking a tusk could be very painful, and if an orc got an infection he might even die from it. Since the tusks are right in front of his face, there would be a good chance of them getting hit in battle. He might be self-conscious about his tusks and worry that people think that he's just a dumb animal-like barbarian.