I have discovered several adornments during the course of the game and according to the description, adornments can only be worn by monsters. But what are they for? Do they give stats or passive abilities like accessories? If yes, what does each of the adornments give? This doesn't seem to be explained very clearly in the game.
They're purely for cosmetic purposes (who doesn't want a flower to put on their tonberry?), and serve as just a generic collectable item.