Player elimination occurs in multiple-player games (>2) when a player can be eliminated from the game and play continues without the eliminated player. The typical examples of games that provides elimination are Diplomacy or Risk (where a player may be defeated) or Monopoly (where a player may go bankrupt and thus be eliminated). There are also games where achieving the win condition will eliminate you from the game and the last person remaining is the loser. An example for this would be Palace.
Player elimination does not include two-player-only games where the goal is to defeat the opponent, e.g., Chess.