A pursuing unit that moves into contact with the battlefield edge moves off the battlefield. They're so caught up in their pursuit of the foe that their momentum carries them clean off the battlefield!
Unlike troops fleeing the battlefield, however, such pursuers are good and keen to come back to the fray. Accordingly, we allow them to re-enter the board in their next Movement phase, using the rules for Reinforcements. The unit is placed back as close as possible to the same point from which it left the battlefield, in the same formation. Remember that it needs to face directly towards the battlefield and have all of its rear rank touching the battlefield edge. It's often a good idea to leave a model from such a unit in order to mark the position from which it left the battlefield (a standard bearer is ideal).