Definition of check behind
A check behind is when the pot is played in a multiway, i.e. with several players. You are last to speak on the flop and there are 5 of you in total on an A-5-K flop. The 4 players before you check. You have an average hand and decide to check. Being last to talk after the flop in a multiway pot where everyone else has checked and you don't have the initiative gives you the option to check behind. This is often a play that is made out of caution since bluffing 4 players is usually a very risky play, with your chances of success being almost zero. In this situation we would say that "the button has checked behind after all players in the hand have checked".
Initiative and check behind
Usually, when a player with the initiative checks after the flop, we say he checks back instead of cbet (not check behind). If the player does not have the initiative and is not "supposed to bet" (players with the initiative often bet) then we say he checks behind. The expression is also used more often when there are several players in the hand.