The Band of Regeneration is an accessory that slowly regenerates health at a rate of 0.5 per 1 second (10 Health Points). The Band of Regeneration can be found in UndergroundChests.
Before the 1.0.4 update, there was a bug where the Band of Regeneration acted as a Water Candle. Since the item ID of the Band of Regeneration is the same as the tile ID of the Water Candle, it is likely that the game developers confused tile and item ID.
The band appears to be a heart stuck on a red ring.