Mystery Egg, also known as the Egg, is an enemy in Final Fantasy IV. It contains a monster within, and if enough time expires during the battle, the egg will hatch, revealing a random monster inside. Destroying the Mystery Egg before this happens will prevent hatching, but no EXP or gil will be awarded.
While the Mystery Egg itself has 0 HP, it will take on the HP value of whatever monster is inside. In the PSP version, the egg has whatever weakness/resistance the monster inside has.