Whenever an opponent discards a card, that player loses 2 life.
"This might hurt less if you don't fight so hard. But I doubt it."
Official Rulings for Liliana's Caress
8/15/2010 : If an opponent discards multiple cards (due to a spell, an ability, or the action of discarding down to the maximum hand size during his or her cleanup step), Liliana's Caress's ability triggers that many times.