Back-end it`s a part of the system which is invisible for user but provide content for front-end. Usually it`s an some API, which have input, output, sometimes db. So, from point of view of functional testing it is classical black-box, or gray-box if you have access not only to output, but to DB and/or logs too, or white-box if you have access to code. Difference of back-end testing in non-functional testing: load, endurance, recovery, penetration, installation, configuration, integration.