Durability is the current condition of your armor or weapon. The number can be found in the bottom right corner of an item description, reading X/Y, where X is the current and Y is the maximum.
When this number reaches zero, your item breaks, causing you to lose any bonuses or visual effects said item may have given. Until you repair it, that is. The only time the durability has any effect on the stats from the item is when the item is fully broken (at 0 durability). Until that time, you will still reap the full benefits of that item.
The main benefit to keeping everything fully repaired is that you can quest for extensive periods of time without worrying about any of your gear breaking. It can also help you during boss battles when in a group, as it gives you some leeway in the number of deaths you can handle before your equipment is completely ruined during that fight. Generally, I make it a habit to check my need for repairs upon every visit to town. The sooner you repair an item, the less costly it will be to both your wallet, and your life.