The Island Generator is the castaways only source of electrical power on the island. Using power generated from parts of the Minnow, it's used to power the camera from the Silent Film crate, keep the Cosmonaut's capsule charged as the Professor repairs it, simulate lightning bolts during a recreation of the wreck of the Minnow and to charge the Professor's makeshift telegraph in an attempt to contact NASA. It's possibly used behind the scenes to charge other objects, like the electric record player on the island.