P-3 visas are for artists who teach or perform "culturally unique" art forms. Argentine tango dancers, flamenco dancers and musicians who play traditional folk music are examples of artists who qualify for P-3 visas.
The exceptional artist may choose to apply for an O-1 visa instead of a P-3 visa.
Here is a link to more information about the visas which are available. http://www.battanlaw.com/Practice-Areas/Dancers-Musicians-and-Artists/
Tip: Because the process is highly complex, it is strongly recommended that you hire an immigration lawyer to help you prepare and file your visa petition. The attorney will also help you follow the process through the system, apply for your visa if you are approved, and guide you in your new status in the U.S.