When the screw is tightened, it pushes the ferrule down against the bow hair, which creates friction and prevents it from slipping. This friction also helps to keep the bow hair in place when it is being played. The ferrule also acts as a spacer, keeping the bow hair from coming into contact with the screw. This prevents the bow hair from being damaged or worn down.
Ferrules are an essential part of the violin bow, and they play an important role in keeping the bow in good condition and performing at its best.