Each opponent loses X life. You gain life equal to the life lost this way.
1/1/2011 Players can lose more life than they have. For example, say you're playing a multiplayer game in which one of your opponents has 3 life and your other opponent has 10 life. If you cast Exsanguinate with X of 4, your opponents will wind up at -1 life and 6 life, respectively. You'll gain 8 life.