When players in the offensive zone pass the puck to each other while skating away from the corners, usually using the boards, to get the defense moving and open up a scoring opportunity once a forward feels he can get open in the slot or move it out to the defenseman.
The term "cycling" comes from the circular rotation that occurs when players continue to circle around from the corner, to the half boards and into the slot before repeating sometimes two or three times. This tactic can tire defensemen and confuse teams.
The offensive play used to be very popular with coaches in the "Clutch and Grab" era as ice was tough to come by when defensemen could lock on and hold or hook forwards. It was one way to force teams to possibly take penalties or get out of position.
Even post-2005 the National Hockey League - NHL sees quite a bit of cycling down low to create offense, or at the very least, burn the clock when a team is leading in a game.