This ability essentially places the Paladin at a higher DPS bracket for the duration. It suits Retribution Paladins best due to their already relatively heightened damage abilities, but is useful in PvP and PvE alike as a way of causing huge burst damage in a small amount of time. This spell itself does not trigger the Global Cooldown, but unlike Judgement, is affected by it.
Avenging Wrath is dispellable and easily recognized by enemy players due to the giant golden wings protruding from the Paladin's back, and thus should be used with caution around Shamans ([Purge]), Priests ([Dispel Magic] or even [Mass Dispel]), Warlock's Felhunters ([Devour Magic]), Hunters [Tranquilizing Shot], and worst of all, Mages (whose [Spellsteal] can give them the great benefits of this spell, making them even more powerful). Therefore, think before you use this spell, and time it correctly. If you are fighting a Shaman, Mage or Priest one-on-one, make sure you cast it the right time (could be when the target is affected by [Hammer of Justice] or [Fist of Justice]). Make sure the target has used any stunbreaking cooldowns or trinkets etc. The result, when timed right, can be deadly.
Because of its powerful boost and well-known visual effect, Avenging Wrath is often simply referred to as a paladin's "wings". For example; "he used his wings, so the other guy was killed in two seconds".
Patch 7.0.3 (2016-07-19): Now available to all specializations and can no longer be dispelled. Healing bonus for Holy reduced from 100% to 35%, and no longer increases haste or damage. Damage and healing bonus for Retribution and Protection increased from 20% to 35%.