In fighting game terminology a 'perfect' is achieved by defeating your opponent - that is, removing your opponent's entire health bar - without losing any of your own in that round. It usually results in the player who earned it receiving a nice points bonus, although in 2-player games where score is largely unimportant, it represents one player's complete and utter dominance over another, and plenty of bragging rights.
Street Fighter II, to many the classic one-on-one fighting game, was one of the most popular games to include usage of a perfect, which was also rewarded in the game's bonus stages if a player managed to complete them in the allotted time. It has also appeared in rival companies' games, such as SNK's King of Fighters series.
The term has also crept into other genres of video game, always being used whenever a player has done something especially worthy of note. A good example of this is in Sega's Sonic the Hedgehog 3 (and the Sonic & Knuckles quasi-sequel cartridge), in which a player is awarded a Perfect and a generous increase in points if they can collect every possible ring in the Special Stage. While it is, of course, possible to complete the Special Stage without obtaining a perfect (just as it is in the fighting games from which the term came), the points bonus can make it worth aiming for.