The term "post processing" refers to what happens to an image between its initial capture (on film or a digital camera sensor) and its final display, either as a print on a computer monitor.
In the days of film this consisted of development (to produce a negative), and printing. For snapshots, you sent your film to the corner photolab and got back standard prints, which were processed and printed by a machine. The operator performed only minimal, basic adjustments, if any. Remember that gorgous blood-red sunset you shot on color film? Were you disappointed when the print came back from the lab a sickly yellow? The automatic processor tried to "balance" the colors and couldn't cope with that much red. To get a print close to what you originally saw you'd have to take the negative to a pro lab and have it printed by hand.
The same basic steps happen in the digital realm, but now the camera itself is doing all the work. When you click the shutter on a typical consumer-level camera, it captures the digital equivalent of a negative. Then it applies some automatic processing rules to the raw data and produces a JPEG file, which by its very nature cannot represent accurately everything in the raw image. You might have a small menu of "picture styles" available, but once the style is applied and the JPEG file is created, the raw image is discarded. If
the camera guesses wrong or the image is beyond the capabilities of JPEG (i.e. too much contrast or dynamic range), there's only a little latitude for adjustment after the fact.
This is analogous to the machine prints made by the photolab, with one major exception. With film you can always reprint a negative for better results and keep adjusting until you get the desired effect. With consumer digital the "negative" is gone. It's as if you sent off your exposed roll of film for processing but got back only the prints.
Professional-level cameras (and some higher-end consumer cameras) can and do save the original "raw" image data without any processing. This is the digital equivalent of the film negative, and is a record of exactly what the camera "saw", without alteration or reduction. It contains significantly more data about each pixel in the scene, and with appropriate software the photographer can make adjustments and corrections that are completely impossible when starting with a JPEG file.
This is why I shoot only raw format, and why I allocate so much time
to post processing.