Why is rubbing the skin briskly with rubbing alcohol beneficial?

Beneficial in what way? Alcohol is a relatively good topical antiseptic, meaning it will help to remove some of the germs found on the skin, but don't get the idea it will "kill all the germs". Really all it does is effectively "degrease" the skin and the rubbing will remove or wipe away a lot of the topical germs on your skin. Hydrogen peroxide is a much better "germ killer" if you get a really dirty cut. Pouring alcohol on a cut is torture - it does no real good. Just wash cuts with soap and water, rinse thoroughly, and bandage.

An alcohol rub can lower a child's temperature.