The Durability of an item is a number that shows how much the item is yet undamaged. If you use an item (by wearing if it is armor, or by fighting with, if it is a weapon), there is a small chance that it gets damaged. This means that the item loses a durability point. Note: If armor is worn, but no damage is taken, it doesn't lose any durability.
If you continue to use an item, it will lose more durability points until its durability drops to 0. If the item has no durability points left, it breaks (in Diablo I the item disappears). A broken weapon (with Durability 0) cannot be used to fight. Any broken armor temporarily loses its attributes, if it had any. An item's durability is restored by going to a blacksmith and let him/her repair it.
Some items can gain durability over time due to certain magical attributes. Some special types of items cannot be repaired (being ethereal).
An item can also become indestructable by socketing a Zod Rune within it. This removes the durability counter from the item.