Tires are meant to be round, so obviously flat spots damage the tires' functionality. Tire flat spots are dangerous because one or more flat spotted tires can cause a shimmy or harmonic vibration that makes it difficult to steer your car. They might even cause tire failure and accidents.
By far, the most common cause of flat spots on tires is storage. If a car is left too long in the same place, the contact patch --- the area of tire touching the ground --- can become rigid. This is worse in cold weather and with underinflated tires. Once you start driving again, if you have flat spots, you will likely notice a shimmy or vibration. Then, as the tires warm and the rubber "relaxes," the shimmy might be subdued or disappear altogether, but the tires are still unsafe, especially if they are not properly inflated.
To avoid flatspotting from sitting, use a wheel cradle that distributes weight and holds your tyre's shape. For prolonged storage, put your car on jack stands and store the tires on their sides.
Locking Your Brakes
Locking your brakes up will grind a flat spot in one or more tires. Of course, this happens much more often with race cars than street cars, but it happens on any car if you lock the brakes at speed. The instant your breaking exceeds the traction limit of a tire and it begins to slide, its like running nutmeg over a grate. The instant the wheel begins spinning again, it stops. The difference is, with this kind of flat spotting, you haven't only changed the shape or your tire, but you've removed material from it. In that case, it might have to be replaced.
Like locking your breaks, you can flatspot a tire by sliding your car sideways --- not drifting the back end sideways with the wheels spinning, but actually sliding it sideways. It's essentially the same thing as locking your brakes. The tires are not spinning and they're grinding across pavement as if it was sandpaper. When racing or on the street, it's important to be aware of this kind of flatspotting if you've just had a near-disaster and slid your car. If you're on the street, inspect your tires to make sure the flat spot didn't penetrate the tread. Proceed cautiously. If you're unsure, have them checked out at your local tire shop.