Optical format is a hypothetical measurement approximately 50% larger than the true diagonal size of a solid-state photo sensor.
The use of the optical format means that a lens used with a particular size sensor will have approximately the same angle of view as if it were to be used with an equivalent-sized video camera tube (an "old-fashioned" TV camera).
In a video camera tube, the diagonal of the actual light-sensitive target was about two-thirds the outside diameter, which was the measure used.
The optical format is approximately the diagonal length of the sensor multiplied by 3/2.
The reason it is expressed in inches is historical, dating back to the early days of television.