Electricity can be a very dangerous thing if the electrical current short-circuits. It can start fires and cause unwary people to be inadvertently electrocuted.
This is why people usually put a fuse in any circuit. Sometimes, however, the current in a circuit is too great to use a simple fuse. A fusible link is the mack daddy of all fuses. It is essentially a piece of braided wire that melts and disrupts the circuit before it can cause anything really bad to happen.
You often find them in the ignition systems of automobiles.