How does braking stop a bicycle?

Same as on a car. Applying the brakes means that something stationary is pressed against a moving part. This generates friction, which turns speed into heat.
It produces friction, because when the brake touches the rim of the bicycle, the bicycle slows down. (thats called friction) And after a while the bicycle stops
A stationary part is brought into contact with a rotating part. The resulting friction slows the bike down.