Very simply put, many-body perturbation theory (MBPT) is a way to account for electron correlation by treating it as a perturbation to the Hartree-Fock wave function. It is a rather straightforward application of simple perturbation theory. Usually, one computes corrections to the energy using second-order perturbation theory, which is abbreviated MBPT(2). This is usually also called second-order Møller-Plesset perturbation theory, or MP2. For some problems, MP2 is more reliable than DFT. It is virtually always an improvement on Hartree-Fock.

In principle, one could go up to higher orders of perturbation theory (MP3, MP4, etc), but the computer programs become too hard to write, and the results (perhaps surprisingly) don't necessarily get any better.