This is a term used in football to describe the action of a player leaving their typical assignments and running to the opposite side of the field to take on a different assignment. It is used most often for offensive and defensive lineman. For example, if a running play starts on the right but will proceed left, the right side of the offensive line may run to an area on the left side in front of the sprinting running back. The linemen that ran would be known as "pulling-linemen."
The advantage of having linesman take their blocking abilities away from one side and applying them to the other is it overpowers the defense on one side. By doing this, the offense will ideally open a space in the field for the running back to run up the field and gain yards. In order to successfully execute a play in which lineman pull, the team must have athletic, fast lineman capable of getting to a spot quickly to block a defensive lineman within seconds of the ball being hiked.