Poison is a type of counter that actually goes on the players themselves. Poison counters got their spotlight in Scars of Mirrodin with the ability Infect.
A poison counter
While poison counters don't affect your life number, they don't have to. If you have ten poison counters on yourself, you lose the game, regardless of your life total. The best way to get poison counters on your opponent is to play creatures with Infect. If infect creatures go through to your life, instead, they'll just put as many poison counters on you as the amount of power they have. Creatures with trample and infect will do the same thing: if the blocking creature dies, and there is still more damage left to deal, you can deal the rest to the defending player and deal it in the form of poison counters. You win twice as easily with poison counters, and there's only one way to get rid of them, Leeches.