The burning legion's mission is to be the extension of Sargeras will/motives, by virtue of being coerced through force as well as gleefully accepting whatever power the corrupted Titan bestows upon them.
Sargeras wants to kill all titan world souls as soon as possible in order to prevent Void possessions via old god infection, azeroth has a particularly powerful titan world soul. The Burning legion essentially serves as a planetary wrecking crew and vanguard for Sargeras himself, who can cleave planets in half, literally.
In legion, the Burning Legion will attempt to bring Sargeras to Azeroth through any manner of ways so that he can destroy the planet. Whether it is the last world soul or not is up in the air, but it was the last one the pantheon found before Sargeras turned on them.