Stairhopping is a technique used to kill creatures while having a safe place to retreat and heal.
Stairhopping is achieved by standing right next to some Stairs, a Ladder or a hole with the creatures you want to kill on the floor below or above you. You go up/down, attack, then down/up again when you need to heal.
Since Update 8.41, stairhopping without getting hit is no longer possible. It is still posible to do Ledgehopping with the use of three stacked objects by a ledge to kill monsters and receive no damage.
Using stairhopping is very common for players on PvP worlds for staying alive or waiting for a protection zone block to end while being attacked by Player Killers.