Quarterstepping is a tactic used to gain positional advantage without suffering a loss in overall attack speed. It exploits the game mechanic which allows a small amount of movement after each attack. The goal of quartstepping is to position yourself between the target and the place that the target intends to travel, body blocking them from their destination; this provides increased opportunity to hit (and do more damage) and land criticals (since the target is more likely to move away from you).
Attack the target and, just before the hit lands, click to move in the direction of desired repositioning, then click the attack key (default: [Spacebar]) just in time to initiate the attack again without losing a beat. You can also use keyboard commands to move your character, but this increases the risk of accidentally cancelling an attack before it lands and, in a worst-case scenario, can cause you to become body blocked by your target and rubberband.
This works in exactly the same manner with attack skills as autoattacks, except that attack skills can not be accidentally cancelled by moving prematurely.
 Other Benefits
Because quarterstepping ends the character's attack, a character can use it to execute other actions that would otherwise idle them, e.g. to swap weapons or to move oneself closer to another potential target (which is especially useful in spike calling).