Something I picked up while watching a Pants are Dragon video though I've added some of my own why and what to do instead to the thought process.

As a jungler if you successfully gank a lane (get a kill or push the enemy laner out of lane) and your laner is low you will want to help them clear any enemy minions that are present so that your laner can go back to the Fountain to recharge and buy. This also has the effect of speeding (typically called shoving) your minions into the enemy turret to be killed forcing the enemy laner to miss getting the gold and XP from those minions and doing a little damage to the turret.

One exception this is if the enemy laner has Teleport up. Because this allows them to port back to lane as soon as they respawn. If you shove your minion wave under their turret in that scenario you will leave your laner in a poor position. Low and pushed, which will make them an enticing target that the enemy jungler will likely want to gank.

If your laner is healthy enough then leave the minion wave where it is at. If your laner is low and wants to back then you can hold the lane by last hitting only.