Answer
Low melting point and high resistivity.
Work Step by Step
The fuse material should melt at a relatively low temperature, lower than that at which the wiring material melts. We want the fuse to melt before the surrounding wiring does, which protects the wiring from excess current.
The fuse material should also have high resistivity so that a relatively high amount of heat is dissipated in it (the heat loss in the fuse can be expressed as $P=I^2R$), causing the fuse to heat up and melt when a critical current is exceeded.
