Dielectric strength of an insulator or dielectric medium is given by the maximum potential difference which a unit thickness of the medium can withstand without breaking down. In other words, the dielectric strength is given by the potential gradient necessary to cause breakdown of an insulator. Its unit is volt/meter (V/m) although it is usually expressed in KV/mm.
For example, when we say that the dielectric strength of air is 3 KV/mm, then it means that the maximum PD which one mm thickness of air can withstand across it without breaking down is 3 kV or 3000 volts. If the PD exceeds this value, then air insulation breaks down allowing large electric current to pass through.
Dielectric strength of various insulating materials is very important factor in the design of high voltage generators, motors and transformers. Its value depends on the thickness of the insulator, temperature, moisture, content, shape and several other factors. For example doubling the thickness of insulation does not double the safe working voltage in a machine.