Clay court tennis is sometimes described as a sport within a sport. If you're going to master playing on clay - a surface which is most popular in Europe and South America - you're first going to have to master how to move on clay. That means having the right shoes for the surface, which are specifically designed for running and sliding across the clay granules and dust and will also give you the support and stability you need.
As the ball bounces more slowly on a clay court than on other surfaces, the rallies tend to be longer, so you're going to want shoes that allow you to move with confidence. All the leading players on the ATP and WTA Tours wear clay court shoes when they are on the surface.