Nichrome wire is used as a heating element because it is very stable, even at high temperatures. Unlike other metals, it will not melt even when generating large amounts of heat. Ironically, nichrome actually has low electrical resistance, the property that causes the wire to heat.
Electrical resistance is a measure of how difficult it is for electricity to flow through something. Substances with low electrical resistance are very efficient at moving electrons, while substances with high electrical resistance are poor conductors and can even be used as insulation. When electrons encounter resistance while trying to flow through a substance, energy is lost through heat.
Although nichrome is actually an excellent conductor of electricity, when it is used in heaters, it is wound into long, thin coils. The shape of the wire, rather than the material it is made out of, impedes the flow of electrons and generates heat. This impediment to current is analogous to water struggling to flow through a long, skinny pipe as compared to water flowing freely through a very short, broad pipe.