All you have to do is listen to the theme song -- it's all there! But here it is in a coconut shell: Five passengers went on a boating expedition that was supposed to last only three hours, but there was a storm, and the S.S. Minnow shipwrecked. The Skipper, his goofy first mate, and the passengers set up house on an island and made various futile attempts to be rescued.
True Gilligan's Island aficionados know that there were two versions of the theme song, which was written by George Wyle and the show's creator Sherwood Schwartz. The first version specifically mentions five of the cast members, then lumps two other characters together, referring to them as "the rest." But Bob Denver (aka Gilligan) thought the song should be rewritten to include "The Professor and Mary Ann." Denver may have played the doofus on camera, but he used his star power to get equal billing for his fellow cast mates. He truly was everyone's "little buddy."