What is accelerating P.D.?

Electrons move around a circuit due a difference in potential, because they gain potential energy as they move through the battery and lose this as they do work moving around a circuit. This still applies in an electron gun because there's an electric field present. They gain KE (energy) equal to the potential energy lost moving through the p.d., (the phrase 'p.d.' refers literally to difference in electrical potential energy, and conservation of energy states that it cannot be lost, so is converted to KE instead) given as
KE = electrical potential energy change between 2 points = (charge of electron x voltage) = eV