Anything that's anti-slip prevents things or people from sliding or falling down. An anti-slip mat in the shower can make it a lot safer!
All sorts of things that potentially slide around can benefit from anti-slip technology. Think of anti-slip eyeglasses that stay on your nose, or anti-slip grips for your ski poles or handlebars. During an icy winter, you probably wear boots with anti-slip soles to keep from slipping and falling, and elderly people can also protect themselves from falls with anti-slip surfaces around the house. The Greek anti- means "against," and slip is from a root meaning "slippery."