Electrical motors and other devices can be damaged by getting too much current. Current sensitive relays react when the amperes go over or under a given threshold. Current can increase or decrease and present a danger in many different situations.
When a motor suffers some sort of mechanical failure—broken belt, etc.—it can cause increases or decreases in current. This variance in current can blow out expensive components or lead to a catastrophic failure of the entire device. Relays provide a level of protection that ensures that the devices aren’t damaged because of the surges in current or because of significant drops in current.