Peeling paint presents a real dilemma: it's too small to warrant stripping the entire wall but too big to ignore or paint over.
Certainly you can always prime and paint over an area where paint has peeled off. As long as the remaining edges are stable, it will work. But it's an ugly solution, especially if you're dealing with peeled paint that is several layers deep.
The method shown here fills in the depression with wood filler. It also helps protect those edges of existing paint so that they are less likely to begin peeling again.