Unique Monsters are stronger and have semi-random magical bonuses. Most of the Unique monsters you find will be randomly spawned throughout the game. However, Super Unique monsters will always spawn in every game and in the same location.
In Diablo III, Unique monsters as commonly known are called Rare monsters instead. The 'Unique' title is reserved for special monsters that usually spawn for quests, events or just rarely in the same location, being similar to Diablo II Super-Uniques. Certain Unique monsters, however, aside from the encounters vital to the game's storyline, are certainly in every game. These Uniques can be considered as Super Unique for that reason. Like Champions and Rares, they have affix skills (and sometimes even their own special abilities), but they always have a fixed set of 1 to 4 affixes regardless of the player's level.