A self-tacking jib is an arrangement where a boat can be tacked to the opposite point of sail without adjusting the jib sheet in any way. e.g. you can go from close-hauled starboard tack to close-hauled port tack, or starboard reach to port reach, just by flipping the rudder. The main flips over on its own, and so does the jib.
It is usually accomplished by having a track that is either straight, or shaped in an arc, to which the clew is attached by means of a sliding "car".
The position of the jib is adjusted in or out by means of sheets which either a) control the end points on the track to which the car can travel, or b) a line which runs from the cockpit to the bow, from the bow to the car, and then up from the car to the clew of the sail. When you pull on the line, it pulls the clew closer to the track (for pinching) and when you release it, it allows you to run further downwind.
It sounds more complicated in print than in reality.
A few of the Hobie's have this feature. So do Ideal 18's and a host of larger boats.
The advantage is for single-handled, or lazy, sailors. You can preset the main and the jib to the close-hauled position, and then tack upwind by moving only the rudder to move from tack to tack.
Like a TV remote control, once you've used one, you never want to go back to the old way.