When any piece of equipment reaches +15, it gains an additional ability, which is shown in the item's description. The Equipment also gains an additional ability every 10 levels up to +55. Below is a list of the possible abilities and some notes about them.
Darkness (Unknown Effect, does not seem to do anything so far)
No Encounter (Really, REALLY bad, avoid at all costs.)
2x MP Regen (This actually ADDS 100% MP Regen instead of multiplying, meaning full MP every turn.)
2x EP Regen (Same as above, full EP every turn... yep...)
EP-Retain (EP carries over from each fight)
HP Regen +5%