A backcheck in hockey is how a player attempts to respond to the attacking team's attempt to score. Backchecking is usually done when there's an odd man rush or after the opposing team breaks away with the puck, the defenders then rush back to the defensive zone and use defensive tactics to regain possession of the puck. This is how players transition from offense to defense on quick plays.
When a team loses possession of the puck in the attacking zone they need to be quick to stop players on the opposing team bringing the puck into their defensive zone to score a goal. They can help defend against goals through an effect backcheck.
Players will skate back to the defensive zone and then turn to face opposing players preventing them from having a clear breakaway. An effective backcheck can have multiple defensive players guarding a single opposing player.
Players that are backchecking are coming from their attacking zone to their defensive zone. While skating back, players are usually skating in the same direction as their opponent and once they make it back, they turn around to face and defend them. When backchecking, players have to communicate where they're going and who they're defending. The goal is to get as many defenders back there to help as possible to avoid leaving one the goalie alone against the opponent.
Backchecking is common during an odd-man rush, when there are more attackers than defenders in the attacking zone. In this situation, it could be two on one, three on two or even three on one. Defenders are rushing to their defensive zone to avoid these situations and help out their goalie by getting the puck back before the attacking team gets a chance to score.
When backchecking you'll see players try to get the puck back by moving an opponent's stick, using their stick to get free the puck or simply getting in their opponent's way to stop them from making a goal.