Wrathion has been a figure in WoW since Cataclysm. Questing through the Badlands, we aid a red dragon, taking various samples of black dragon eggs and black whelps and using some kind of Titan technology to cleanse them. The result is a black dragon egg that is free of the Old Gods' corruption. Later in that expansion, Wrathion hatched from that egg and hired Rogues who took part in the Legendary quest chain for the Fangs of the Father (oh! which I just finished!) to help him wipe out every other black dragon on Azeroth. This mission is a success (though the fate of Baron Sablemane, who we saw in Blade's Edge Mountains on Outland remains uncertain.) Wrathion would then try to manipulate the war between the Alliance and the Horde, trying to bring about a decisive victory of one over the other so that one would absorb the other. To his dismay, the Alliance agreed to allow the Horde to exist as a separate entity with its own Warchief. While the cooperation between the two factions to take down Garrosh was along the same lines as Wrathion's goal, it was not the kind of permanent union that he had hoped to accomplish. The two factions went back to rebuild, still eyeing each other with distrust, instead of integrating their powers to become one Super-Faction.
Wrathion helped to orchestrate Garrosh's escape from his cell in the Temple of the White Tiger and flee with Kairoz, Zaela, and some of the Infinite Dragonflight to Draenor-B, thus setting in motion the events of Warlords of Draenor.
Spoilers to follow.
Wrathion has always been trying to save Azeroth. Even if his methods have been brutal and manipulative, his goal has always been the safety of his home planet. In Legion, we will encounter him once more. His vision of the Burning Legion advancing on Azeroth has now come true, and we are not perhaps as unified in our efforts as he had hoped we would be.
The Iron Horde was part of his plan, but Garrosh screwed it up by setting the Iron Horde against Azeroth in a bid to take revenge on the Alliance that beat him and the Horde that ousted him. The Iron Horde was never meant to stop with just Draenor B. There was a potential infinitude of Hordes to be created, as Kairoz revealed to Garrosh shortly before the latter killed the former. The Iron Horde we faced would be the first, and they would go from universe to universe, recruiting Horde after Horde - an Infinite Horde, if you will.
The Burning Legion has incredibly powerful magic, but their real advantage is that their numbers never really decline. The only demon we know for a fact has been permanently destroyed was Tichondrius. Archimonde, even after being destroyed on Mount Hyjal, was apparently able to resurrect in the Twisting Nether. The beings that we face and call demons are actually just avatars of the true demonic souls in the Nether (which actually explains why the more powerful the demon, the more power you need to summon it - summoning a demon basically means constructing a body for it.)
So if the Legion (almost) never loses a soldier, that means you can never beat them by numbers - if you limit yourself to one finite universe. The Infinite Horde (my term, not theirs as far as I know) would have been the solution. The Legion might have their infinite lives cheat on, but they still have a finite (if enormous) number of troops. There's only one Twisting Nether, and that might work as a limiting factor on how many demons can exist within the Burning Legion (for now let's ignore questions of what happened with all the alternate-universe Archimondes and Kil'jaedens when they became demons.)
So you can see how this admittedly extreme action is in line with Wrathion's goals. He wants to beat the Legion at all costs, and dealing with an Infinite Horde? That might be worth it. The Orcish Horde (when they're not, you know, fighting for the Legion) are often cruel, fascistic brutes, but they at least seem to want there to still be a world to live in.
Kairoz is obviously the person who can make all this happen - as a Black Dragon, Wrathion doesn't have any expertise in time-way manipulation. But the Infinite Dragons? What's their role in this?
We really don't know exactly what the deal is behind the Infinite Dragonflight. We do know that they're corrupted versions of the Bronze Dragonflight, and their leader, Murozond, is a corrupted version of Nozdormu. But how they came to be what they are, and what they really want, is kind of up in the air.
The dungeon journal description of Murozond lists him as being corrupted by the Old Gods. I would think that this would have made him as big a threat, if not a bigger one, than Deathwing (I mean, being able to manipulate Time has got to be more impressive than being the Warden of Earth.) When we faced Murozond, he was blocking the timeways to the past to prevent us from getting the Dragon Soul to use on Deathwing, or at least that's what we believed was happening. His death ended that effect, allowing us to go to the War of the Ancients to retrieve it, and thus allowed us to prevent the Hour of Twilight and kill Deathwing.
We've only really faced the Infinite Dragonflight in a few places - there's a rare enemy (who used to be a friendly one) near the Caverns of Time entrance, and we find them in Old Hillsbrad Foothills, the Opening of the Black Portal at the Black Morass, in the Culling of Stratholme, and at the Bronze Dragonshrine (both when visiting it in Northrend and in the post-apocalyptic future of the End Time dungeon.)
What's odd is that we often get the Infinites arguing that they're the ones doing what's best for the world. Sure, in Old Hillsbrad Foothills, they just kind of want to kill Thrall, but in the Black Morass dungeon they talk about how they want to prevent all the horrific wars that would come thanks to the invasion of the Horde into Azeroth. In the Culling of Stratholme, they try to stop Arthas before he can go to Northrend and become the Lich King. Murozond even claims that the Hour of Twilight would be a better apocalypse than the "True End Time," which could very well be the result of this Legion invasion.
It is listed in-game, but I have my doubts that Murozond was truly corrupted by the Old Gods. I even have my doubts that he's truly the future version of Nozdormu.
We know that there are multiple universes - we've been spending the last year in a different one (and will be there until Legion drops.) End Time depicts a world where Deathwing succeeded (and wound up dead, because he was really serious about killing everyone,) and it's there that we kill Murozond. But if there were just one timeline, then the event in which Murozond died wouldn't even exist, so...
Why do they call themselves the Infinite Dragonflight? Sure, the name just sounds cool, but why call themselves that?
It's implied that the Draenor we built our garrisons in was always around. It wasn't split because of Garrosh's actions and Grom's rejection of the demon blood. There were other differences that could not have been the result of the time-travelers' interference, like the fact that Rulkhan is alive or that Garrosh was never born.
But what if we're wrong about that? These things could not have been the result of Garrosh's meddling, but it could still have been a split-off timeline - as long as someone had just gone back a little farther.
There are two theories for how multiple universes could work. Either they all branch out at points where there could be more than one outcome, or they all exist eternally in parallel. The latter version is the least messy, but both versions allow you to avoid the kinds of paradoxes that arise if there's just one timeline.
So if it is a branching multiverse, with each new universe being spawned by a fork in the temporal road - one timeline where Grom drinks, the other where he doesn't, for example - that means that changing the past is literally the same thing as creating an entirely new universe.
And each new universe means more recruits for your army. You have that Infinite Horde ready to assemble, but first you need to split the timelines. And whose job is that?
The Infinite Dragonflight.
Is it reckless? Yes. Could there be totally unintended consequences? Yes. Do you endanger potentially infinite lives? Absolutely. And is this the sort of thing that could easily grow out of hand, perhaps being manipulated by beings that are on a whole other order of magnitude of power and intelligence? You betcha.