A jibe, Also spelled "gybe", is turning your rig around and sailing in the other direction by heading downwind. This seems to be the most natural method for turning around.
In my opinion there are four jibes that make up the core Jibes. Whether you are racing, wave sailing, swell riding, or just slogging, then one of these jibes will be good by you. Start with the general purpose Standard Jibe then learn the Carving Jibe so you can keep the board planing all day long. In the waves the Snap Jibe will be your friend and when racing use the Step Jibe.
The Intermediate Jibes are mild variations of the core jibes. Foremost is the functional Laydown Jibe which not only depowers the sail but also allows you to have good vision because the sail is out of the way. The Laydown can also be performed by removing the front hand in the One Handed Laydown Jibe. Next is the required and ubiquitous Duck Jibe used by all sailors including Pro Sailors. The Duck Jibe itself has many variations including Aerial, and Backwinded versions. The Jump Jibeinstills an aerial theme while the Ghost Jibe rearranges the foot work.
The Tricked jibes are more complicated jibes and involve greater board control, balance, and sail skills. The easiest to learn is the classic Backwinded Jibe. I learned the Essex Jibe;a long time ago and this move involves a sail duck followed by a Sail-Body-360. Of course the classic Monkey, Reverse Monkey, and Donkey are all pretty fun when dorking around. Others include the Jibe Pirouette, Jack, and Boomerang.
As far as I know "jibe" is the American spelling, English/Australian is "gybe".