How do braces fix the overbite?

Braces Align Teeth. If your overbite is off because your teeth are in the wrong positions, then braces can move your teeth into the proper positions, resulting in a pleasing smile & proper bite. If, however, your overbite is off because your upper and lower jaws aren't aligned correctly, then braces will have limited success. Bone problems cannot be corrected predictably with braces in adults. In kids often they can.
Force. The "medicine" we use in Orthodontics is Force. Braces are a handle on each tooth to facilitate transfer of force to the tissues that support the teeth. This allows growth and development dental and skeletal supervision in children, dental repositioning in adults. See a qualified Orthodontic Specialist for information as it pertains to your specific problem set.
Overbite. In layman's terms, an "overbite" typically refers to the upper front teeth sticking out horizontally, further than the lower front teeth. An orthodontist defines an "overbite" as the vertical overlap of the upper front teeth over the lower front teeth. They are very different situations unfortunately with the same name. It's best to have an exam with an orthodontist to determine the problem.
Moving teeth. If not severe repositioning the teeth can correct the overbite.