Attack refers to a command the player gives to either his character or his pet.
Attack initiates general melee combat with the currently equipped weapon(s). Your character will continue to attack until the attack action is toggled off, an attack interrupting action occurs (turning the wrong way, getting stunned, etc), or the target is dead. The speed at which you attack depends on your equipped weapon(s). Some actions (self-heals) do not interrupt an auto-attack.
Also see Wand Usage section of Wands for how auto-attack works with wands.