When we hurt our fingers, we immediately put them in our mouth. When another body part is hurt, we put our hands on it. Why is that ?
More interestingly, sometimes it even seems to work and reduce the pain. How come ? Is it a kind of placebo effect ? Is it that the nerves that are used to convey pain are also the ones that tell us about warmth or sense of touch, and the more immediate stimuli (i.e. something is touching your skin here !) overrides the other one (i.e. your body is damaged here, ease up) ?
Rubbing the area can increase blood flow, too. It seems to smooth out the nerve firing. It is also beneficial to pull an injured body part close to your body, to protect it from further injury.
If my fingers get hurt, my reaction is to either grab them or place my hand under the upper part of my opposite arm, so that my fingers are between the side of my ribcage and my upper arm. This is a very good technique to protect the injury.