Delta Pokémon are a special kind of Pokémon whose type and appearance differs from their normal counterpart.
In the game
Shortly after the events in the Cult of Darkrai base, the player decides to start a Pokémon journey and seeks out Professor Sylvan to obtain a Starter Pokémon. Upon entering Professor Sylvan's lab, the player interrupts a conversation between Reukra and Professor Sylvan about Delta Pokémon. Reukra suggests that the player and Damian take the Delta Pokémon as starters.
There are other Delta Pokémon the player may encounter throughout their journey. It is not known if these Pokémon have been altered artificially or through a natural mutation, but it is hinted by Reukra that some may be the result of experiments led by the Cult of Perfection in their search for a perfect Pokémon.