Charge conjugation is the mathematical operation that turns an elementary particle into its antiparticle. The process of reversing the property of particles that determines the difference between a particle and its antiparticle is usually denoted by the symbol C. In the case if electrically charged particles, the equivalent antiparticle carries the opposite charge, which is the origin of the term "charge conjugation".
The interaction obtained by applying the C operation to a possible particle interaction is also allowed in the real world, by the laws of physics. In most cases, it follows exactly the same law as the reverse operation. But because of a very small asymmetry in the workings of nature, processes involving the weak force are not quite invariant under C. For example, although beta decay (in which a neutron decays to produce a proton, an electron, and an antineutrino) has a counterpart (in which an antineutron decays to give an antiproton, a positron, and a neutrino), this decay isn't exactly the same as the interaction described by applying charge conjugation to beta decay itself, and takes place at a slightly different rate. What these means is that the antimatter world isn't quite symmetry to the matter world, even allowing for charge conjugation.