Variable Player Powers is a mechanic that grants different abilities and/or paths to victory to the players. To illustrate, here are some notable examples.
In Ogre, one player controls a single powerful piece, and the other plays many weaker units. The net effect is a balanced game.
In Cosmic Encounter, each player is assigned a random special ability at the beginning of the game. Although each player has the same victory goal (establish colonies on five planets in other players' systems), their abilities enable differing means to the end.
In Here I Stand, each player controls a political power with unique ways to score victory points. Some focus on military conquest, some on religious influence, etc.
Player powers may change throughout the game, as in Small World or Sunrise City.