Windsurf shoes are a lot like climbing shoes in some respects. They tend to be thin, waterproof, and have good grip, to keep you planted on the board. Footwear is highly recommended for a couple of reasons. The first is safety, many popular windsurfing destinations are also the natural habitat of jellyfish, one of the less pleasant denizens of the ocean.
A jellyfish sting will hurt a lot no matter where it occurs, but human hands and feet have some of the most tightly bunched areas of nerve endings in our bodies. This means that any sting or cut on the foot is felt more keenly than it would be other places. To avoid the possibility of an agonizing sting to the foot, windsurf shoes should be worn if there is even a chance of jellyfish in the area.
Another good reason to wear windsurf shoes is for performance on the board. The shoes are designed to give you better grip on the board than bare feet provide. This grip comes in handy when performing maneuvers, because you can only put as much force on the mast as you are able to support with your stance. A solid stance with firmly planted feet gives you better control, and allows you to perform more difficult maneuvers than a sloppy or slipper stance does.