Quilling

First make sure that your hog is actually quilling. If you suspect otherwise, read the section on mites and/or the section on dry skin.

What is quilling?
Think about teething. Quilling is the same thing only with quills. A hedgehog’s baby quills will fall out and new ones (bigger ones with a final color) will grow in.
Quilling usually occurs when a hedgehog is between ages eight weeks and six months. Quilling can, though, occur earlier or later. Quilling lasts anywhere from two weeks to two months, depending on the hedgehog. Some hedgehogs only lose a few quills a day, some lose up to 50!
During quilling, most hedgehogs become grumpy (imagine if you had needles poking through your back) but it is still important to take them out and play with them. Otherwise they will learn that they can get you to leave them along by being grumpy. You should handle them more gently than usual though, because their back will be sore.
What can I do about quilling?
While you can’t stop quilling or speed it up, there is something you can do to help your hog. Every 4-5 days, you can give it a warm(make sure it isn’t hot!) bath. (Read the section on bathing) The water will help soothe them. It may also be a good idea to add some oatmeal to the bath. The most common way of doing this is putting it is a sock, dipping the sock in the water and letting the oatmeal mix with the water, then removing the sock. That way there is no mess.

The following information has been copied with permission from www.hedgehogcentral.com

Of all of the features of your pet hedgehog, probably none stands out more than than the quills. When you really stop to think about it, they really are quite remarkable. They are the main means of defense that a hedgehog has against predators, but they serve some other rather useful purposes as well. Although scientifically described as being modified hairs, each of the roughly 7000 quills on a hedgehog's back is far more complex than any hair possibly could be. Rather than being solid inside, each is filled throughout with complex network of air chambers. Not only does this make them very lightweight and strong, but it also helps to prevent buckling and breakage. At the base, the quill narrows to a thin stem where it enters the skin and is firmly anchored in the muscle tissue by a small, ball-shaped follicle. At the opposite end, the quill narrows to a needle-like point and is bent slightly back to provide maximum defense should a predator be interested in having hedgehog for lunch!
When attacked, it is the contraction of the two large muscles that run down either side of the hedgehogs body that cause the quills to be raised in defense. When those two muscles are contracted, (much like pulling the draw strings on a purse) they pull against the ball-like base of the quill, drawing it into an upright position. Since the muscles pull different quills in different directions, they tend to crisscross one another, forming a near impenetrable barrier.