Our skin cells divide rapidly in order to maintain a protective barrier against infection. The outer skin layer is called the epidermis and contains mostly dead cells that contain keratin. Keratin is a tough fibrous protein found in hair, skin, and calluses, and acts as a protective coating.

The epidermis cells are constantly undergoing mitosis so that the outer dead cells containing keratin are rapidly replaced as they fall off, which occurs after so many days. Then the newer living cells start producing keratin, lose their cellular contents, and die, and the cycle goes on.

The skin acts as a barrier to infection; therefore, it is constantly renewed and repaired.

I'm guessing my skin cells aren't undergoing mitosis continuously, because I'll be 70 yrs old this week, and my skin is getting old. Or maybe mitosis just takes longer in my old skin cells. But my skin cells are still undergoing mitosis fast enough to keep an unbroken layer of skin over my body.

Our skin is exposed to the outside world, where it encounters air that dries it out, and getting rubbed by our clothes, and injuries caused by things outside our bodies. The cells inside our bodies don't have to experience any of those things. That's why our skin cells undergo mitosis continually, to protect our bodies from these things, and from harmful microbes.

Here's what the National Institute of Health says about skin when it gets injured:
"...injured cells at the site of a wound send 'go' signals to the surrounding skin cells, which respond by growing and dividing and eventually sealing over the wound."