The name is a contraction of "variable resistor"* ? however its construction is quite similar to that of a capacitor. Just like a capacitor it consists of two metal plates separated by an insulator. When the voltage between the two plates reaches a certain value, the insulator breaks down and admits the flow of current.
Varistors have a capacitance and could be called capacitors; likewise, all capacitors have a breakdown voltage. The difference is that in most capacitors, breakdown is highly undesirable, and usually results in the destruction of the device. Varistors on the other hand are designed to repeatedly withstand breakdown. While the insulator is in breakdown, it still has a non-zero resistance, and hence heats up while conducting current. If the size of the transient pulse (often measured in joules) is too high, the device may melt, or otherwise be damaged. For example, a nearby lightning strike may permanently damage a varistor.
Important parameters for varistors are response time (how long it takes the varistor to break down), maximum current and a well-defined breakdown voltage. When used in communications lines (such as phone lines used for modems), high capacitance is undesirable since it absorbs high frequency signals, thereby reducing the available bandwidth of the line being protected.
Another method for suppressing voltage spikes is the transient voltage suppression diode (TVS). There are two significant differences between a varistor and a TVS: