Commander is a format where players construct 100-card decks, with each card except basic lands appearing no more than once. Players also choose a legendary creature (or Planeswalker card in Commander 2014) to be their “Commander” (also known as a “General”), which begins the game in the “Command Zone”. Each player’s deck is based and built around their Commander’s colours. In addition to the same losing conditions that exist in a normal game of Magic, each player starts the game with 40 life points instead of 20, and a player may lose if he or she is dealt 21 or more total points of combat damage from a single Commander throughout the game. Commander is most commonly played in groups of four, but larger groups do happen. A one-on-one variant on the Commander rule set has been rising in popularity.
Commander also has its own “banned list” of cards, separate from any other format. A list of the recommended banned cards in the format can be found on Wizard’s official page here