From Bulbapedia, the community-driven Pokémon encyclopedia.

The Mirage Pokémon (Japanese: ミラージュポケモン) are holographic Pokémon, seen in a Pokémon Special The Mastermind of Mirage Pokémon. They were created by Dr. Yung, a Pokémon scientist who invented a machine that generates Pokémon holograms.

These Pokémon essentially have no weaknesses and are invulnerable to attacks from normal Pokémon. They are able to know and use any move, even one they would naturally be unable to learn. This is comparable to a Pokémon in the main series games which is hacked, such as a Mewtwo with Quick Attack, a Beautifly with Aeroblast, or a Walrein with Meteor Mash.

Notes

• The Mirage Pokémon is also the unofficial nickname for Mew, although this is mainly a coincidence because in Japanese, Mew is the まぼろしの ポケモン illusory Pokémon while Yung's mirages are ミラージュポケモン mirage Pokémon, which uses the English word "mirage".
• In Pokémon Mystery Dungeon the Mirage Pokémon is Ho-Oh.