Postprocessing is just any effect that processes the entire rendered screen. The most simple effects are stuff like color correction, tone mapping, blurring, sharpening, etc. These are fairly simple to implement using a shader with a couple of texture samples and a tiny bit of math. You also have a couple of anti-aliasing postprocessing shaders out there, with FXAA being the simplest to get going. Then there are more advanced postprocessing algorithms, like screen-space ambient occlusion, motion blur, depth of field, bilateral blurs, custom multisample resolves, temporal supersampling, etc that are much harder to get right and may require multiple fullscreen passes and tricks.
If you have any specific questions I’m sure I can answer them.