In the process of painting you focus your attention on a subject that is at your fingertips. If you do it with enough concentration, it will ignore the extraneous noise, unpleasant thoughts and worries. This is a very useful skill that will be useful in situations where you need to briefly forget about your physical or emotional pain.
Coloring helps the child to learn how to control the scale of his hand. Please note that when the baby is just started to draw he does not monitor the boundaries of the sheet, and the picture is not painted on the outlines, and even beyond.