Aqua socks or water socks are made for swimming. They are designed to provide some protection from rough or sharp objects as you swim or when you enter or leave the water.
But, their best purpose for sports like scuba diving, free diving, and snorkeling is to help maintain body heat in cooler waters. A good aqua sock provides excellent insulation while not interfering with your kick while swimming.
A good aqua sock can be used as an insert inside of your diving flippers to prevent rubbing and chafing and to keep your feet from getting too cold. Although aqua socks are shaped like regular socks, they are made from fabrics like neoprene for use in the water. And, they are made for swimming!
If you are looking for something to wear when around the water and want protection from walking on hot sand, slippery surfaces, and the like, you want a water shoe which is similar to a water sock in that it breaths well but has a sole like a regular shoe.