Here is my version:
Not really sure how it comes into play in aquaria, I see it mostly in waste water applications. Basically when you are trying to oxidize an organic material, you might introduce something like chlorine, or sodium hypochlorite (bleach). There is an actual exchange of electrons as the organics are broken down. The ORP probe picks up on that exchange and reads it as a milivolt measurement. As the oxidation process consumes more and more of the organics, the milivolt reading drops.
Simply put, ORP is used as a way to tell when adequate oxidation has taken place.