Photo "Editing" versus "Manipulation"
Of course, many people don't think of what they do as photo manipulation, rather, as photo editing. While any change to a photo technically qualifies as photo manipulation, this is a common distinction to make.
Photo “editing" generally consists of smaller changes that do not change the image in any fundamental way. Virtually all digital photographers partake in this sort of photo manipulation, from removing red eye to adjusting curves to playing with color balances. Sometimes, it's that the photographer made a mistake composing the shot and the manipulation is just to fix it, to straighten a crooked horizon or to lighten an underexposed photograph. Others, it's to increase the aesthetic qualities of a photo, to saturate the colors of a sunset or to remove a distracting branch from a skyscape. No intention to deceive, only to please.
Where precisely this crosses over into what is more popularly considered photo “manipulation" is a subjective line, one that varies greatly by photographer. Generally speaking, photo manipulation is when you have conglomerations of multiple photos, or if the photo has been changed beyond reasonable recognition.
Photo manipulation is done for a number of purposes. More infamously, it is for political or sensational purposes. Notorious examples of this vary from a “blacker" version of OJ Simpson's mugshot to Soviets erasing political figures from photographs once they fell out of favor. Indeed, the first known case of photo manipulation is one of Abraham Lincoln made to look a bit more trim.
However, photo manipulation is also an art form in its own right. Fire spirits, literal lionfish, a little boy fishing on a crescent moon, all are examples of high amounts of photo manipulation as fine art. Beautiful and foreign images may be created from the familiar, and the techniques involved in doing so require every bit as much skill as photography proper.