A shorty wetsuit is designed for swimming/surfing/etc… in warm waters during the summer. It is the lightest type of wetsuit available because of the fact that it doesn’t really have to keep you that warm. Most people start wearing a shorty wetsuit when the temperature gets to about 72F (22C) or when there is a cool breeze which gives you a chill. They are also popular on cloudy days when you just want to stay a little warmer so you can surf longer.
When the water temperature is above 72-74F (22-23C) most people don’t wear a wetsuit at all and typically either just put on a wetsuit top or vest. Of course, each individual is different and some will want to wear this type of wetsuit even in warmer waters.
The reason this type of wetsuit is called a shorty is the fact that it has short sleeves for the arms and legs. Essentially you are about as covered as you would be if you were just wearing shorts and a t-shirt, but of course the wetsuit is tighter fitting. The thickness of the neoprene is normally about 2 millimeters and often has flatlocked stitching which is not 100% waterproof.
If you want to learn more about which wetsuit goes with which water temperature and what are the factors that influence the feeling of cold check this article.