World of Warcraft Chronicles Vol. 1 Spoilers to Follow.
At this point, the statute of limitations on the spoilers for the books I think has passed - if you haven't gotten the book by now, you'll probably just want to find out these things through gameplay and internet osmosis.
I'm almost hesitant to keep marking these as spoilers, but just out of courtesy, I'll do it again this time.
So let's talk about Cosmology.
Right at the beginning of Chronicles, we find out about six fundamental forces - basically three pairs. There are inner systems as well, such as six Elements and then the two realms just barely outside of physical reality.
We're going to talk about the lower-right one, which is Death.
Each of these fundamental forces has an associated type of magic, as well as sort of "prime representatives." Death is affiliated with Necromancy and the Undead. This latter notion is actually pretty amazing when you consider that this puts the ranks of ghouls and skeletal warriors up with Titans, Wild Gods, and Void Lords.
This fact has fueled, for me, speculation that the Lich King as an entity is actually far more powerful than we had previously thought - that Kil'jaeden did not truly create him, and that Ner'zhul was not exactly the "original" Lich King, but that instead the Deceiver tapped into some fundamental and incredibly powerful force and merely gave it form. We know that despite being creatures fundamentally associated with Chaos and Fel Magic, demons have been known to tap into other forces that change their nature in interesting ways, like the Dreadlords Sargeras found who had fallen in with the Shadow and the Old Gods (there's also a Nathrezim/Dreadlord in Legion who has apparently gone over to a very surprising force indeed, but I won't say any more out of fear of spoiling things,) so it's not outside the realm of possibility that in the mutilation of Ner'zhul, Kil'jaeden tapped into a fundamental force normally outside the demesne of the Burning Legion.
As we found out at the end of Wrath, "There must always be a Lich King." That's pretty shocking given that the Lich King has only been around since the Third War. But it starts to seem more possible if we consider that perhaps, the Lich King, or rather the thing for which the Lich King is an incarnation or avatar, is actually something that has existed since the universe began. Consider, for example, the fact that the Lich King seems to have a personality that is independent of the three individuals who have served that role. Ner'zhul is not in there anymore, nor Arthas, so why should Bolvar be anyone but his normal self, albeit undead-by-default?
Closer to physical reality, but not quite there, we have the Elements. There are the four familiar alchemical ones, but also two additional elements - Spirit and Decay. Spirit, known as Chi to Pandaren Monks, serves as a kind of facilitator for the four physical elements to exist in harmony. Notice how on Draenor, the local Elemental Lords are not only free in the physical world, but work quite well together. On Azeroth, this is not the case, because the World-Soul within the planet has drawn on this "fifth element" to help it grow, leaving the local elementals without that social lubricant that keeps their kind from ravaging other worlds. Decay is sort of a "Sixth Element," though in a way it's simply the absence of Spirit. The best representation of Decay is, I think, the practice of Dark Shamanism, which sets aside balance and harmony in favor of force, and we saw a lot during the Siege of Orgrimmar and Battlefield Barrens of how this practice leads, essentially, to pollution and environmental damage.
The next level down, hovering just beyond physical reality, there are two realms. These are so close to reality that they actually mirror it. One gets a lot more press, and is called the Emerald Dream. Our few sojourns into the Dream have shown us mostly a familiar landscape, albeit one that is supercharged with life (where it hasn't been corrupted by the Emerald Nightmare.) The Emerald Dream seems to be a place of eternal renewal, and the Wild Gods are bound to it.
On the flip side, there's the Shadowlands. And while this is a name we've barely ever heard, I strongly suspect (frankly, I believe it, because it's almost explicit in Chronicles,) it's one that we visit on a pretty regular basis. The Emerald Dream is the realm of life, and the Shadowlands are the realm of death. When a player character dies in game, his or her spirit shows up in a shadowy version of the area that he or she died in. It's a desaturated version of that familiar world, but looks the same other than the crazy skybox texture.
The Shadowlands are explicitly where mortals go when they die. It's a sorrowful place, but unless some other force, like the Naaru if you're lucky or the Burning Legion if you're not, decides to take your spirit with them to their plane of reality, it seems you'll be there forever.
In Chronicles, we learn that Keeper Odyn - who was Azeroth's original Prime Designate - balked at the idea of empowering the Dragon Aspects to protect the world, as Proto-Dragons were not Titanic creations (in fact, they're apparently descended from elementals - though that might just be all organic life on Azeroth that isn't Titanic.) He far preferred the Vrykul, who were one of the top Titanforged Warrior races.
Odyn engineered a culture among the Vrykul that strongly favored glorious death in battle. He forcibly transformed his most trusted Vrykul follower, Helya, who was something like a daughter to him, into the first Val'kyr, whose explicit purpose was to travel between the physical world and the Shadowlands, taking the spirits of Vrykul who had fallen in glorious battle and bringing them to the Halls of Valor - Odyn's personal wing of Ulduar (that he had had Helya relocate to the sky after he cut ties with the other Keepers over the whole dragon thing.)
Helya brought these souls to Odyn, and Odyn granted these champions new bodies made out of metal - freeing them from the Curse of Flesh. These "Valarjar" would be his alternative to the Dragon Aspects, at least until Helya and her Val'kyr managed to rebel. Helya locked Odyn and his Valarjar in the Halls of Valor and then created her own afterlife realm called Helheim, where she effectively had her own champions, who you'll recognize as the Kvaldir.
I don't know how the Lich King managed to get his hands on the Val'kyr - he may have simply made new ones the same way that Odyn had, or perhaps if he is actually the avatar of the true God of Death, he might have simply had power over them because of Death's prominence within the Shadowlands - to which all Val'kyr are bound.
But one thing we do know is that there were some Val'kyr who yes, had broken away from Odyn's control but did not want to serve Helya either. These val'kyr decide to sort of carry on Odyn's mission of finding and reviving the greatest heroes that Azeroth has to offer, but they aren't limiting themselves to Vrykul and they don't bother with sending them up to the Halls of Valor to get a new body made of metal. They just bring them back roughly where they were.
And that, ladies and gentlemen, is who the Spirit Healers are. It's possible that there are extra complications for Death Knights (maybe Undead/Forsaken characters as well) and Demon Hunters (given that they are partially demonic, and thus their souls are "safely" sent to the Twisting Nether upon death,) but when your character gets killed in game, you wind up in the Shadowlands because, well, that's just what happens to people who die in the Warcraft Universe. But rather than wandering as a shade forever, the Spirit Healers pluck you up and tell you to get back out there into the physical universe and fight the good fight again.