The articles "a" and "an" mean "one." It implies one of many.
In the sentences you provided, the word "a" is used as an indefinite article. It is used to refer to a non-specific or generic item or concept. In this case, when you say "a sports club" and "an art club," you are simply referring to one of many sports clubs and one of many art clubs that exist in your school. It does not specify any particular club, but rather represents any club of that type.
