How it worksToughness is a measure for how much Damage a creature can take in a turn before it is Destroyed. A creature is dealt damage through combat, spells, and abilities. Creatures battling will each deal damage equal to their Powers to the other creatures toughness. If a creature has equal or more damage marked on it than its toughness, then it is destroyed. A creature's toughness is the number on the right side of the box in the bottom right corner of a creature card. Many spells can modify a creature's Toughness or Power, some only for a single turn, and others for as long as a permanant is in play. Some spells apply counters which affect a creature until removed. During the cleanup step, every creature's toughness returns to its printed value (modified by its counters and other permanants, such as enchantments, equipment, and specific abilities).
If I attack with a 5/2 like Summit Apes, my opponent can decide to block with a 0/6 like Wall of Tanglecord. Since the Wall has a toughness of 6, the 5 power of the Apes will not be able to destroy the Wall because the 5 damage it will deal is less than the 6 toughness of the Wall, resulting with the Wall having 5 damage marked on it until end of turn. If however I'd play Lightning Bolt on his/her Wall of Tanglecord, it deals 3 additional damage, for a total of 8 damage (in the same turn). 8 Damage is enough to destroy the wall.