The Delta Episode (Japanese: エピソード デルタ Episode Delta) is a mission following the player's first completion of the Hoenn League in Pokémon Omega Ruby and Alpha Sapphire.
You unlock the Delta Episode after beating the Elite Four and Champion for the first time. After doing so, the Delta Episode starts. Also, I would like to note that the Delta Episode is one thing, there are not multiple Delta Episodes.
Source (Contains spoilers for the Delta Episode. You have been warned.)