Cloning is an Integrity deck specific effect card. When used, you will receive a copy of a selected ally monster to your hand. This should of course usually be used on your best cards, such as Undyne or Asriel Dreemurr.
As of Beta 11.0, you will now gain an exact copy with the same ATK, HP and Cost. Status effects like Silence, KR and Paralyze will not.