Varistor ratings are given for two different conditions - when they are off (current up to 1mA) and when they are on (current at the clamping current, many amps). You need to keep within the voltages given for the off condition for the vast majority of the time so that the varistor is not dissipating much power continuously. Therefore the varistor should have higher a.c. or d.c. (as applicable) voltage rating than the maximum continuous voltage at that point, so that they don't start to turn on. Due to manufacturing tolerances, the components vary from part to part so they give min and max values for some parameters - you would want the min peak voltage rating to be above the maximum continuous voltage at that point in the circuit to be sure it is off.
Under transient pulse conditions, the varistor turns on and conducts high currents. Again there is a variation part to part, and also varistors I-V characteristics change after each pulse, depending on the energy of the pulse. The max clamping voltage is the maximum that the varistor will clamp the voltage to when it is conducting the max clamping current. You probably want this as low as possible so that you can use lower voltage rated components downstream of the varistor, but this is a compromise with the both the Off State rated voltage and the pulse current due to its effect on the lifetime.
For example, the Z130PA20C is rated at 130V AC RMS which might make it suitable for a typical 110V AC supply, assuming you never expect the 110V AC to get to 130V. It will remain in the off state as long as the RMS voltage stays below 130V RMS or 184V peak according to the datasheet. It will start to conduct between 184V peak and 220V peak, at 1mA. It clamps the voltage to 325V at 100A for a standardised pulse. Therefore the rest of your circuit needs to be able to survive 325V for these microseconds. If this is too high, you will find that larger diameter varistors, or multilayer varistors, have flatter clamping characteristics.
Some manufacturers give much more information, for example Littelfuse, which defines all the terms of page 16 of this document.