This definition is actually copy-pasted from Liquidpedia (a StarCraft 2 wiki), but the definition is essentially the same in Diablo:
"Stutter Step is a technique where you order a unit to move right as its attack animation starts. This way it will deal damage but instantly start moving again, allowing you to keep up with fleeing units and attacking again."
Basically, you attack and then instantly move, then the second the animation for the attack ceases, you can attack again and move again. The result is that you will attack at essentially the same rate as somebody who is standing still except you will be moving.
Side note, in other games, the idea is taken even further to "cancel" inputs you already did. The cancelling of a move or spell can either come before the move/spell has gone off or after, depending on the game and your input. It's the basis for most fighting games and is prevalent in a lot of genres. And is super fun too!
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"Stutter Step is a technique where you order a unit to move right as its attack animation starts. This way it will deal damage but instantly start moving again, allowing you to keep up with fleeing units and attacking again."
Basically, you attack and then instantly move, then the second the animation for the attack ceases, you can attack again and move again. The result is that you will attack at essentially the same rate as somebody who is standing still except you will be moving.