Class enemy is a term used in communism to refer to a person or social group of people who are seen as "enemies" of the revolution.  Class enemies of communism - in the traditional sense before Stalin ran away with it - would be the upper and Middle classes of society, rich, land-owning people who were referred to as the Bourgeoisie.
As cited above, Stalin went completely awol with the idea of class enemies, and used this as an excuse to systematically orchestrate the killing of millions of his own countrymen throughout the 1930s.
Example; you are a rich farmer whose door gets kicked down at 3am by the NKVD (Soviet Secret Police), and they demand all your grain. If you say no, you are labelled a class enemy, because you are preventing your grain from being shared between all, and will consequently receive a bullet in your head and quite possibly have your family raped.