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. Their name is always highlighted in golden (D2) or purple (D3).
In Diablo III, Unique monsters as commonly known in Diablo II 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 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.
In very rare cases, Unique monsters may have extra skills, such as triple attack speed or additional elemental damage, that are not available through affixes.