Mirage Island is an island located on Route 130. It is occupied by only one type of Pokemon, the pre-evolved form of Wobbuffet, Wynaut. The Wynaut range from Level 5 to 50, so try to catch as many as possible. What makes this island unique is that it's the only place in Hoenn that you'll be able to obtain the 36th Berry, the Liechi Berry. The Liechi Berry is used to make the Gold Pokeblock, which is the rarest and strongest Pokeblock.
You may notice that when you go to Route 130, Mirage Island is nowhere to be seen. That is because Mirage Island only appears when you catch a Pokemon that has a certain hidden number to it (called IV's). Once you get the Pokemon with that IV, you must go to Pacifidlog Town and walk to the very bottom, then go to the right-most house.
Once inside, there should be an old man at the right of the house looking out a window. When you talk to him, he'll tell you if he can see Mirage Island today. If you don't have to the right Pokemon, keep going back with different Pokemon to see if Mirage Island appears.
If the old man does say he can see Mirage Island, go to Route 130 and the island will be there. Be sure to collect all the Berries and Pokemon you can because once the day ends, Mirage Island will dissapear again and you'll have to try and get the right Pokemon all over again.