It's where all mesh data is rendered to the G-Buffer. Data such as world space positions, normals, diffuse, material IDs, etc are stored in various render targets, the G-Buffer. Then lighting is performed per pixel. It also lends itself very well to screen space techniques such as ambient occlusion, reflections, DoF, subsurface scattering, etc because you have all the data in screen space. Instead of your renderer being bound by the amount of polys, you are now only limited by fill rate, because all intensive GPU effects are applied per pixel of your render target/frame buffer/back buffer, not per vertex per mesh. This is how lots of lights are able to be rendered.
Post process means apply effects to the overall image, I.e. Your render target after you have drawn your meshes. Post, means after.