Post-processing is a process by which a photo is reworked to produce the artistic vision of a photographer. The term "post" implies that this work is done sometime after the photograph is taken, not "in-camera" — although some post-processing may be done very shortly after, still in the field.
Analog and chemical processes are used to work film, while digital processes and tools are used to work digital images. For many photographers, reproducing the original scene exactly as it was, with as much natural color accuracy as possible (or tonal accuracy in the case of black and white photography), is the holy grail. For many others, post-processing is the chance to add unique style and flare to a natural scene, finger-printing their work. This can involve conversion to black and white, tone mapping, duo-tone conversion, contrast adjustments, and the application of creative color shifts.