Post processing is the act of taking your images from the camera and modifying them to further enhance their look and feel. In the days of film, this would be done while the film was being developed, or most often when a print was being made. Among other techniques, they would dodge to darken, burn to lighten, and filter to improve contrast. Many of those concepts were translated into computer software, so when you use a program like Adobe Photoshop, you are applying similar effects to your images without all of the chemicals and film.
Post-processing to clean up the background.