A debuff is generally a non-permanent attribute added to a unit, affecting it directly or indirectly negatively for a period of time. Such an effect is the Barbarian War Cry ability that lowers opponents defense or other statistics. It applies to targets in an area of effect, but they retain this "debuff" even when they move out of that area.
Another example is the Wizard's freezing abilities, which makes units immobile for a few seconds. If the target dies with this debuff on it, it will be crushed into icy bits instead of falling over like a corpse.
Buffs are generally applied by a character or monster of caster type, or some effect in the game like a trap of some sort.
The direct opposite of a debuff is a buff, that works similarly, but has direct/indirect positive effects on the recipient.