That's not too hard. There are plenty of real-life animals that want to be eaten. They're either parasites, or the hosts of parasites, whose behavior is modified by the parasite that they carry.
Of course, since you want the interaction to be mutually beneficial, your animals won't technically be parasites, but their ancestors could have been. It's also fairly common for parasites to evolve into mutualistic relationships with their hosts.
The reason for a parasite to want to be eaten is simple enough: it needs to get inside another animal in order to continue its life cycle, whether that's to trigger a metamorphosis of some sort, or because it's eggs can only hatch in a certain kind of host, or whatever. The trickier part is figuring out how eating the parasite turns into a benefit for the eater.
The obvious one is that eating the former-parasite provides the same benefits that eating usually provides--energy and nutrients--in sufficient degree to offset whatever resources the now-symbiote drains from the host. Perhaps, for example, there is a creature with a multi-stage life cycle with morphology alternating each generation, such that one generation requires a certain other animal (or class of animal) as host, and the alternating generation is free living. Now, just make the free-living morph capable of eating stuff that its host animal can't natively digest, and the host/predator species will be able to expand its nutrient base by eating the free-living generation in exchange for hosting its eggs. This is basically the same kind of relationship that humans have with goats: goats turn unfarmable land into meat and milk for humans, and in exchange for letting us eat them, we breed and take care of the goats. Pigs are in a similar situation--they turn garbage into meat, and we help them reproduce in exchange.
Another option might be starting with a mind-altering parasite, like, e.g., toxoplasma (except an animal version of it--perhaps something like an intestinal worm that has similar psychopharmacological effects as the real-world protist), and figuring out a way that its psychological effects could become beneficial. This could be completely accidental; for example, the aforementioned toxoplasma causes rats to become unafraid of cats, so that the cats will eat them, because it needs to live in cats to reproduce; in humans, it (allegedly) causes the host to become more fond of cats as well... even though cats don't typically eat humans, so its a dead-end for the parasite! Although toxoplasmosis can also cause psychological illness, one could argue that making humans fonder of cats is actually beneficial, as keeping cats around means that the cats eat rats, which cuts down on disease transmission. Maybe if more Europeans had toxoplasmosis, we would've avoided the Black Plague! Make your fictional parasite capable of reproducing in its accidental host, and you have a mutually beneficial relationship there.
Taking a more direct approach, it's possible that a parasite ends up having incidental effects on an accidental host (not the one that it originally evolved to control) that induce immediately beneficial behaviors. Just off the top of my head, it's not hard to imagine a parasite that, e.g., induces an attraction to water and bathing (because it wants to be spread through water), which directly results in improved hygiene for the host.
It is also possible that a host animal evolves over time to accomodate for the effects of carrying a parasite, such that removing the parasite actually results in pathological conditions. If, for example, the parasite is psychoactive, and the host evolves to adjust its production of neurotransmitters to function normally when under the influence of the parasite, then removing the parasite will result in abnormal function in the modern host. At that point, the former parasite is really acting as a mutualistic symbiote, helping to maintain the hosts neural function. One could argue that humans already have this sort of relationship with a lot of common microbes--lack of exposure to common microbial infections results in deficient immune function. Parasites-turned-symbiotes could also produce vitamins, useful toxins which are stockpiled by the host and used against other animals, etc.
You may have noticed that of the behavior-modification examples I came up with essentially come down to improving competition against other parasites (diseases). That's accidental (I'm sure with sufficient thought one could come up with positive behavior modifications that are also useful for a parasite, and don't have to do with parasitic competition), but that idea can be exploited more directly: perhaps the parasite is good enough at fighting off competing infections that dealing with that one parasite is a better idea for the host than leaving itself open to a wide variety of other infections. This, of course, can easily be combined with evolution through tolerance to dependence on the parasite for normal function. Note that humans also sort of already have this relationship with a lot of gut bacteria! If they get into the wrong places, it's really bad, but we like having them in our intestines because they keep the other baddies out.
Ability to carry a parasite could also be subject to sexual selection, in which case the parasite that makes an animal want to get eaten could benefit its host enormously by increasing its reproductive prospects before it gets eaten. If the parasite has obvious behavioral or physical effects, those may end up acting like a peacock's tail; a peacock's tail is a horrendously expensive feature that severely reduced the bird's ability to avoid predators, and its only purpose is to show off to peahens that I'm so incredibly awesome that I can get away with growing this impractical thing and still be alive. Your animal would be showing off a similar attitude: I'm so incredibly awesome I can survive and thrive despite obviously carrying this parasite. Now, that's something of an unstable situation because there would be pressure to evolve the expression of similar features without having to actually carry the parasite (essentially lying about fitness to get more / better mates), but it could become a stable mutualism if combined with evolution towards accommodation of and dependence on the parasite's presence, for any of the reasons described above. Then, you could end up with a "parasite" that wants its host to get eaten so it can complete its life cycle, and a host animal that wants to get eaten (after having lots of babies) because it wants its parasite to complete its life cycle--because if the parasite goes extinct, so will the host species that has come to depend on it! (For vitamins or neural function or parasitic competition or whatever combination of things.)
So, there you go. Just try to think of all the ways that parasites can evolve into mutualistic symbiotes. Then, start with an animal parasite that needs to be eaten to complete its lifecycle, but does not kill the host, or a microbial parasite that makes its host animal want to be eaten, and evolve that into either an animal symbiote that wants to be eaten, or an animal that wants to be eaten as a side-effect of carrying a microbe (or whatever), but benefits sufficiently from its symbiote before that happens.