Attack refers to a command the player gives to either his character or his pet.
Player auto-attack
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.
Pet
Attack is a pet command that instructs the pet to attack its master's current target. This is the only way to get a pet in passive mode to attack.