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You might know about the heating effect of electric current. So, in the wires too. Fuse wires act as a limit to the electric current flowing through it. It prevents damages or overheats, fires etc by fusing and turning off the circuit as when as there is a sudden increase in the circuit. That's why fuse wires have high resistance and low melting point, so that they can melt on time before any unexpected situation is faced. 
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The fuse is supposed to be the weakest link in the circuit. The circuit is rated to handle a specific load current. The wire and insulation rating of the circuit is governed by this specific load. If this load malfunctions and the load current becomes higher, the fuse is there to break the circuit. So fuse wire is used in an electric circuit. :)
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