The full system is pretty complicated, but the gist of it is that if you lose to a finalist somewhere along the way, you enter a repechage (second chance) bracket that allows you to fight for the Bronze. The higher up in the original bracket you reached, the less fights you have to deal with in the repechage bracket.
There are two repechage brackets, each constructed by the losers to the different finalists, and in each one a bronze medal is awarded to the winner.