Pulling in football is when a player leaves their usual assignment to do something different on the field, such as covering a different player. You might hear this phrase as a player being "pulled" or "pulled out of position" to another area of the field.
Pulling is typically used by guards in football. It occurs when a guard runs behind the offensive line to the opposite side of the field. A guard would pull from one side of the field to the other, often pulling a defensive member with him.
Sometimes, pulling a defender is enough of a tactic to create an open space for a pass, but other times the guard pulls to block a defensive lineman unexpectedly. The pull is often referred to as a sweep, because a guard sweeps from one sideline to the other. This strategy is actually used in many sports as a strategy to evade defenders or create open space in the playing area.
In order for a guard to excel at pulling, he has to be a very quick and agile runner. He must be able to cover distances in a short amount of time or else the pull won't be successful. Since he also does quite a bit of tackling, he must be a strong player with enough force to bring down an opponent.