The Angel Statue is a decorative statue depicting an angel. Like other statues, it can be found Underground. Unlike other statues, it can also be found in chests. It has no purpose beyond decoration.
This may be a reference to Weeping Angels in the popular TV series Doctor Who.
The Angel Statue sprite is used for missing items and items with missing/invalid sprites. This is most often encountered in mods, but it can also be found in standard Terraria when an invalid item such as the Zapinator is in the inventory.
Prior to becoming a placeable statue, the Angel Statue literally had no use. Because of this, the Angel Statue has become the subject of several jokes among the NPCs, particularly the Merchant and the Dryad.
Though the other NPCs claim it as "junk," the Travelling Merchant voices the uses of an Angel Statue ("They slice, and dice, and make everything nice!"), despite (as far as the Terraria community knows) not selling the item.