Wither is a static ability that changes how a source deals damage to creatures. Instead of marking damage, a source with wither puts that many -1/-1 counters on the creature it damages. So a 3/3 with wither that deals 3 damage to a 4/4 leaves it as a 1/1, because the counters permanently reduce its power and toughness. Damage to players is unaffected; wither only matters when creatures are involved.
In play, wither makes creatures excellent at shrinking opposing creatures over time. A creature hit by wither stays smaller even after the turn ends, unlike ordinary damage. This can chip away at large threats, set up favorable blocks, and make creatures with wither dangerous in combat because every point of damage permanently weakens the opposing creature.
