Most species of animal, especially mammals, have a special skin cell the produces melanin, which is responsible for the color of their skin, but orcs are generally depicted as green creatures and, of course they are another race too, but for this question, assume they are mammals and are green. What will be the evolutionary trait that causes it and is there any real benefit should they form civilization resembling our modern society?
Flamingos are originally born grey but become pink due to eating brine shrimp, which have a natural dye called Canthaxanthin from their diet brine shrimp and blue-green algae. If an orc was like a flamingo (lol) then they could become green by eating certain plants/animals that have natural green dyes or colours that make green such as blue and yellow. And don't worry that a flamingo is a bird, it happens in humans as well. An example is the Paul Karason, who turned blue from drinking colloidal silver to treat his dermatitis, and the blue skin from excessive colloidal silver ingestion is permanent. Another is eating carrots or pumpkin in excessive amounts turning your skin yellow. So just make your orcs eat something green a lot to make them green!
There are two green mammals, actually. And both are sloths.
In this case, it's a type of algae, which is only present on sloth hair and is a symbiotic relationship.
But you aren't talking fur, you're talking skin. Still. You can use this as a model and you'll want to look at bacteria and fungus present on all our skins.
Humans can get a condition called Tinea Versicolor that causes discoloration and spots. Basically it is a fungal overgrowth.
You can take this concept and run with it. Here's how I would do it.
There are different breeds of fungus or bacteria present in orcish populations. The conditions of their skin is a perfect home for them and may give some benefit to orcs. They might be born a greyish color (of which there are plenty of examples in the animal kingdom) but as they pick up the fungus in their tribe, they gain coloration.
Depending on the particular fungus their skin can turn blue or green as they age, and they may even get freckles of an alternate color or from colonies that are more intense. Their starting color, which would range from a very light grey to almost black will also determine what kind of bacteria or fungus can live there.
They may also bathe in material that encourages the growth, and may have "tan lines" because it could react differently to sun.
The advantage is up to you. You can look to the sloths, it can help with sun screening their delicate hides, or even help to heal and toughen upper layers of the skin.
If it is fungal, certain jobs and contact with certain things may kill the fungus--that will be up to you as to what. You might even have their toenails be a brighter or different shade. In humans a blue or green toenail would mean disease, but for them, it means that they are healthy.
There could be various diseases/medical conditions that mean a loss of pigment, or an overgrowth.
An overgrowth could be temporarily advantageous, toughening their skin, making them nearly unstoppable in battle, but shortening their lives.
Just using reality as a jumping off point into the fantastic! The science can be partially based in reality, but since you are talking about a species we don't have on this planet, you can really do whatever you like, as long as it makes sense and is internally consistent. The orcs themselves aren't likely to know what the mechanism is.
If one orc joins another tribe, they might slowly change in color, if that fungus is dominant and can kill the original, after a lot of contact with the other tribe (especially intimately). For example, dark green can be a stronger fungus than the light blue. So a dark green orc might never turn blue when they join the a light blue tribe, but after years they might gain a more teal tone (especially if they marry a blue). But a blue might quickly become green. They could all be green, I'm just spitballin' here. Once a colony is established on their skin, it might not ever change--that's up to you. Such a system could lead to prejudices of course and could be interesting socially.
I liked Fleon_'s note about diet. Let's add some more...
Perhaps their skins are occupied by symbiotic algae which synthesize some vital nutrient for the orc. The green is just a side-effect.
Could be that the orcs evolved in an area of dense underbrush, and the camouflage was useful.
Might be the opposite ... they evolved in a very non-green environment, and the green is a sexual display (a la peacocks), advertising that the orc in question is so very tough that he doesn't need any stinkin' camouflage.
Heck, I'll just toss this one in. It is a well-known fact that orcs begin their lives as photosynthetic pollywogs living in ponds and puddles. The retained the green coloring because it's coded by the same allele as a very valuable trait (e.g. tendency toward mindless, cartoon-like violence). The green has little effect in their adult lives, though I'll say they do enjoy them some sunbathing!
- How could I forget polar bears? They have hollow fur for buoyancy, and occasionally the fur gets colonized by algae. Here's a nice discussion of same: https://www.quora.com/Why-does-a-polar-bears-fur-turn-green . Do orcs have fur?
In world of warcraft, orcs are born with grey skin, but it turns green when they are exposed to fel (demonic) magic.
Trolls are green because they have symbiotic algae that photosynthesis and give them better stamina than one would expect.
A simple evolutionary reason would be camouflage. Just like many animal's fur is colored in a way that hinders detection, the skin's color can evolutionary adapt to improve camouflage as well.
Preconditions for this is an environment rich in green's, and a sufficient time span between orc's ancestor's losing their fur and the present.
The only reason green pigment is rare in mammals is most mammals can't see green, so mammals lost the "green" pigments pretty early. It all started because existing pigments could not make hair green, the blue pigments (tybalt blue) used in skin and feathers don't work in hair,(most animals make green by combining blue and yellow) so if mammals had wanted to be green they would have had to evolve a new pigment, without color vision there is little reason for this to happen. Note this is why green still occur in eyes. The existence of better color vision in primates has led to a greater diversity of coloration they have blue skinned primates, but they still can't get blue or green hair. It is entirely possible they may evolve a new green pigment (that is how they got better color vision than other mammals after all), it could even be a mutation of an existing pigment. Maybe they don't make red or yellow pigments anymore instead making new pure green pigment.
As for why this mutation would spread you have three options, although you could combine these as much as you like.
Camouflage, maybe they live in a jungle or somewhere else green blends.
Sexual selection, maybe it is novel enough that mates find it attractive instead of repulsive, considering all the other weird things that sexual selection has produced this one is easy.
maybe the new pigment is actually better at protecting the underlying tissue than the previous pigment. maybe it reflects the ultraviolet end of the spectrum better which is what makes it green.
The effect on their culture will be minimal. Although if you include #2 they may find non-green skinned people look sickly or ugly.
I really like the Warhammer 40K answer: The Orks aren't really green-skinned but they have plant-like organelles that undertake photosynthesis which turn them green. These feed their Ork host excess carbohydrates in exchange for a place to live and easier access to nutrients. The extra energy makes Orks better warriors, stronger, faster, and with greater endurance and increases their rate of healing letting them shrug off wounds that should be lethal in just a few weeks.
Less of a biological than a social factor, but perhaps Orcs get tattooed with green ink - and get more tattoos the more successful they are as warriors. Similar kind of idea to ancient Picts painting themselves blue before battle with woad dye (see here for more info: http://www.woad-inc.co.uk/history.html).
The only reason we see green Orcs is because we only ever encounter them in battle, and never in any domestic environment - their natural skin colour could be bright pink, for all we see of their non-warrior citizens.
Since orcs tend to live in damp, dark environments which would support all sorts of bacteria/fungi you could argue they evolved copper stores in their epidermis as an antimicrobial