The Cloak Psynergy is a Utility Psynergy introduced in Golden Sun. An Adept can obtain it if he or she is equipped with the Cloak Ball item, which you receive from Babi in Babi Palace following the Colosso Finals. It is of the Mercury element.
The Cloak Psynergy causes the party to turn invisible while in a shadowy area. They will always materialize in light, however. It is used and required to complete the Lunpa Fortress sidequest, where it is used to sneak past patrolling guards in an instance of stealth gameplay. It is also used in Crossbone Isle, specifically the fourth floor, and that will allow you to progress through that floor's puzzle involving statues that block your path if they detect you. In that room, using both Cloak and Halt will also allow access to a chest containing the immensely useful Storm Gear.
The Cloak Ball and its Psynergy can appear in the inventory of Isaac's party in Golden Sun: The Lost Age if any form of data transfer is used. However, there isn't a single instance in the second game where the Cloak Psynergy is actually usable or useful.
The Lost Age