One of the first psychologists who in the early twentieth century used the coloring mandalas as a relaxation technique was Carl Gustav Jung. He prescribed his patients coloring mandalas as part of the therapy.
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.