If the music you write is commercially recorded, you'll want to be able to collect money for the public performance of your song.  This is why one joins a performing rights organization.

A "performing right", under US Copyright law, extends to the copyright owner the right to perform the musical composition in public.  The copyright owner may grant the performing right to another party.

The users of copyrighted music pay a fee to performing rights organizations so that they can perform a copyrighted song in public.   A concept of a "public performance" includes live performances, records, videotape, film.  A performing rights organization licenses the public performance of copyrighted musical compositions.

Radio or television stations obtain a "blanket" license from a performing rights organization to play any of the works in their catalog. Considering the sheer number of songs in performing rights organizations' catalogs, this makes sense.

Performing Rights Organizations:

BMI Web Site
ASCAP Web Site
SESAC Web Site