Circuit breakers and fuses are important safety devices in any electrical grid. Though they perform the same function, there are advantages and disadvantages to each.
A fuse contains a length of filament which melts when exposed to an abnormally high current, breaking the circuit. Fuses are one-use only, however, and must be replaced.
A circuit breaker is a mechanical switch which "trips" when current faults are detected, and can be reset by cycling the switch off and on.
As a circuit breaker is a complex mechanical device, outfitting an electrical panel with breakers is more expensive than using fuses.
When a fuse fails, it can simply be unscrewed and replaced with another of the same type, as long as you have spares on hand. If a circuit breaker fails, you'll have to remove the breaker and wire in a new one.
When replacing a fuse, you need to take care to ensure the replacement is rated for the same amount of current. Using a fuse rated for too much current is a fire risk, and using one rated for too little will cause the fuse to blow prematurely.