A fuse is a thin piece of wire designed to carry a limited electrical current. If you try to pass a higher current through the wire, it'll heat up so much that it burns or melts. When it melts, it breaks the circuit it's fitted to and stops the current flowing.
An MCB is a better alternative to a Fuse since it does not require replacement once an overload is detected. Unlike fuse, an MCB can be easily reset and thus offers improved operational safety and greater convenience without incurring large operating cost. An MCB functions by interrupting the continuity of electrical flow through the circuit once a fault is detected. In simple terms MCB is a switch which automatically turns off when the current flowing through it passes the maximum allowable limit. Generally MCB are designed to protect against over current and over temperature faults (over heating).