To stand out is to attract attention, either for the way you look or behave, or because you perform better at something than other people do. If you wear your mime costume to school, you'll definitely stand out.
Your pink hair and rainbow tights will help you to stand out in a crowd of sports fans or businesspeople, while a conservative suit would make you stand out in a group of circus clowns. You'll also stand out from your entire math class if you're the only one to get an A on the midterm. Someone who stands out by displaying excellence is sometimes called a standout.