What we learned in Chronicle and what is now being gradually peppered in in-game is that the purpose of the Burning Legion - the whole reason Sargeras decided to burn away the universe - is that he fears the corruption of the Void.
Azeroth is the most important planet in the Warcraft universe because it is essentially the egg out of which the greatest Titan who has ever existed will one day emerge. Azeroth is not an it, it is a she (meaning the Tauren religion is totally right! Granted, all the good-guy religions in Warcraft are mostly right - we know that Elune is truly a goddess, though what exactly that means in a cosmos of Titans and Void Lords remains elusive.)
Sargeras fought demons originally - creatures tied to Fel magic, which is the embodiment of chaos, as opposed to the Titans' preferred magic style, arcane, which is an embodiment of order. In fact, there's a quest for scribes where a demon hunter explains that the tattoos they use are arcane magic that is meant to help them keep control of the chaotic fel magic within them. (I've got a whole nerdy theory about why "respectable" mages use frost magic that deals with thermodynamics, but that's a post for another time.)
Yet when Sargeras pursued the Nathrezim, he found that they were practicing a whole different kind of magic - shadow magic, the magic of the void. The Nathrezim had gone to serve entities on a planet where a Titanic world-soul was being fully corrupted by the void. The entities doing the corrupting? Old Gods.
Yes, the Old Gods are actually a kind of biological weapon created by even greater forces of evil called the Void Lords. The Void Lords are apparently so completely alien that they can't really manifest within our reality, and so they created the Old Gods to go where they could not.
Sargeras wound up cleaving the corrupted planet and the embryonic Titan in two, angering the rest of the Pantheon. Sargeras quit their company over this issue.
Later, the Titans discovered Azeroth, and to their horror, they found that it, too, had been infected with Old Gods - four, to be precise, which you'll recognize as Y'Shaarj, N'zoth, Yogg-Saron, and C'thun.
The Titans created stone and metallic giants to wage a war against the Old Gods and their Black Empire. In the midst of it, Aman'thul, the oldest of the Pantheon, physically plucked Y'shaarj out of the planet, tearing a deep wound in Azeroth that proved that it would be too dangerous to simply kill the other Old Gods and also left this gaping wound as the Well of Eternity, which would lead to the transformation of Yaungol into the Tauren and Trolls into the Night Elves.
Yet the Titans succeeded in containing the threat, keeping Azeroth's soul safe from the Old Gods by imprisoning them.
When the Aggramar sought out Sargeras to tell him that there was another path, and that this Titan that would be greater than any of them would now be safe from the corruption, Sargeras responded by murdering his friend.
Sargeras returned to Mardum, where his demonic captives had been kept, and offered them a choice - serve him or die permanently. The demons naturally agreed to serve. Sargeras shattered Mardum, releasing the demons and thus infusing himself with fel magic. He waged a war against the Pantheon with this new Burning Legion and slew them all.
So Sargeras killed his own people - his fellow gods, essentially - and has waged a many-thousand-year-long campaign to destroy the universe - to purge the universe of anything that could be corrupted by the Old Gods.
It's clearly evil, but there's a demented logic behind it.
But given what we've seen of the Burning Legion, it raises some interesting questions.
The first one is: why all the cruelty? Why does the Legion corrupt people and revel in betrayals and madness? If its purpose is simply to wipe out the universe, why doesn't it manifest as a constant barrage of hellfire on any world they touch?
I suppose one explanation for this is that while Sargeras might simply be callous (or even regretfully) purging world after world, the soldiers he has enlisted do not have his noble-if-warped intentions. He didn't create his own Titanic constructs in order to purge the universe. He recruited infernal beings who he had spent countless aeons fighting against. We know that Sargeras' two top lieutenants were once mortal eredar, and it's very possible that every demonic race was at one time a mortal one, and that they have simply been corrupted so much by fel magic that they cease to be humanoid.
But the other question is this: why is the Burning Legion using all this shadow magic?
Xavius proclaims in the Guardian Druid artifact quest that he has been empowered by the Old Gods. Yet he's a demon, working in tandem with the Burning Legion (there's a doomguard leading the assault on the Temple of Elune in Val'sharah, backed up entirely by Nightmare creatures.) The Nightmare is, fundamentally, the product of Old God corruption (specifically Yogg-Saron's corruption of Vordrassil in Grizzly Hills.)
Isn't something like the Nightmare exactly what the Burning Legion was created to purge from the universe?
And we see the Legion using tons of shadow magic. We see them using Void Walkers, which are not, technically speaking, demons at all - as we saw in Shadowmoon Valley, they're more accurately aberrations, as they are linked the void like the Old Gods (in fact, probably more purely.)
Again, we have a couple explanations:
The first is similar to my explanation of the cruelty of the Legion - Sargeras might be in charge, but his soldiers do not share all of his views. The demons are happy to cause destruction wherever they go, and they're not too picky about what kind of magic they use. The Natherzim, after all, were happy to serve the Old Gods when Sargeras first found them.
Another is that we, after all, use magical powers we consider "evil." We employ Shadow Priests, Warlocks, Demon Hunters, and Death Knights, yet just because a Shadow Priest sprouts tentacles if they've been in Void Form long enough doesn't mean that they're serving the Old Gods - in fact, they're often fighting against them. A player Demon Hunter is 100% opposed to the Burning Legion despite using similar magic. Thus, the Legion might simply be using shadow magic as a means to an end that involves defeating the beings most closely associated with said kind of magic.
But the third explanation I can think of probably makes the most sense. Sargeras might claim that his Burning Legion is meant to keep the Void Lords from corrupting the universe with some Dark Titan, but in fact, Sargeras is merely jealous. Aggramar brought him news of a future Titan that would be greater than any existing Titan - greater than Sargeras himself.
So maybe this dark task is just BS. Sargeras doesn't want to euthanize the universe to prevent its corruption. He just doesn't want to be less than some greater entity. And so he doesn't care what happens to Azeroth as long as it dies. And any code of ethics or principles get thrown out the window - Sargeras just hates Azeroth for being better than him.