Dielectric strength is the electric field value above which an insulating material stops insulating and a discharge occurs. It is expressed as a gradient, in kilovolts per millimetre, or as the breakdown voltage for a standardised electrode gap, which is the usual form in oil testing.
It is the parameter that sets how much voltage a piece of equipment actually withstands, and it falls with moisture, with suspended particles and with ageing of the material. In transformer oil, for instance, a few parts per million of water can halve it.
The typical test raises the voltage between two electrodes separated by a standardised distance until the arc strikes, repeating the sequence several times and averaging. In SF6 the strength is about three times that of air at equal pressure, which is why it is used in compact switchgear.