In Hold'em, the button refers to the player who is last to act in each betting round after the flop and--unless heads up--third last to act before the flop. The button is said to have positional advantage and players are usually willing to play a wider range of hands from the button than from any other position.
When a player in late position raises and all players yet to act fold, it is referred to as buying the button. The raiser then has positional advantage throughout the rest of the hand.