A players life total is an indicator of the status of the game. Players start the game with 20 life, and the game is over when a player has 0 or less life. There are several ways to lessen someone's life total. When a Creature attacks, it deals damage equal to it's power to the defending players life (If that creature had no blocking creatures assigned to it.) Instant and Sorcery spells such as Lightning Bolt can directly damage a players life total. These are called bomb spells. Players can also gain life from certain spells and from abilities like Lifelink, which allows you to gain life whenever a creature with the Lifelink keyword deals damage. Life gained is equal to the amount of damage dealt.
Life "counters" are not like Counters that you place on Permanents. Instead, life "counters" act as a way to assist in tracking your life total in-game so you don't have to actively remember what your life total was, which prevents confusion. Life counters can be many different things, from a 20-sided die (these come in Fat Packs or at gaming stores) or a smartphone app, which can track life counters and poison counters alike.