There are also other reasons, mainly cosmetic.
If you have poor hygiene, the teeth under the bracket isn't exposed to food, plaque, or acids produced by bacteria... while the other areas of your teeth are. When the braces are removed, you'll have straight teeth... but you'll have some really awkward discoloration of your teeth. The enamel that was not protected by the bracket will be etched, scarred or have cavities.

This discoloration is caused by acids breaking down the minerals on the surface of your teeth (called decalcification).
Brush after every meal, floss daily and be certain to brush before going to bed, as the protection of saliva slows down during sleep. It is also important to cut down on sugars, and sticky foods, maintaining a healthy diet will allow a long happy lifetime with your beautiful smile!