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