Beta Testing is done after alpha testing.
Testing done by the potential or existing users, customers and end users at the external site without developers involvement is know as beta testing.
It is operation testing i.e. It tests if the software satisfies the business or operational needs of the customers and end users.
Beta Testing is done for external acceptance testing of COTS(Commercial off the Shelf) software.
It is done to acquire feedback from mass market, for example beta testing of Gmail.