"Bet you wouldn't mind hiding that scar sometimes, eh?"
Skin may be the largest organ of the body, but it is also rather thin, making it vulnerable to tears. An injury, surgery, or even a burn - possibly caused by a rebounding Unforgivable Curse - can cause a scar.
Scar formation is part of the natural healing process. Keloid scars are the result of overly aggressive healing. They tend to extend beyond the borders of the original injury and are more commonly seem on people with darker skin tones. Burns often lead to the formation of contracture scars, which may even go deep enough and affect muscles or nerves. Contracture scars tighten the skin and can limit movement. Hypertrophic scars are raised, red scars that do not go beyond the borders of the injury.
Not every skin puncture leads to scarring. Those pesky little paper cuts, for example, heal perfectly fine with little to no treatment. Proper wound care, by irrigating with water or saline is extremely important for larger injuries. To prevent a scar from forming in the first place, it is important to keep the wound moist and covered. A layer of petroleum jelly over the clean wound does the trick.
Unfortunately, many scars never completely go away, even in the magical world. For older scars, several products are available to lighten or reduce the appearance of the scar, but these often take weeks to months to see an effect, if any. Most people resort to concealing their scars with their choice of clothing. Mr. Harry Potter, however, has trouble concealing his lightning bolt scar since it is located on his forehead and his hair simply does not behave.
That leaves one last option - have a really, really good story about the scar! No one has to know that you fell and were dragged through ice while walking dogs in the winter if you tell them that you were injured playing volleyball. (Heh, I'll work on it.) Scars become a part of your skin and serve as a reminder of a life event. In fact, a scar might even impress some people or come in handy as a map of London Underground.