From Diablo Wiki
Act Bosses are Unique enemies that stand as the mightest foe in each Act. The plot and quests of an Act lead up to the battle against them, and they must be defeated to advance to the next act of the game. Act Bosses have unique graphics and special attacks unused by any other enemies in the game. They are often featured in cinematics and are always important in terms of lore and story.
See the individual pages for full details.