What is the peculiarity partial discharge?
According to the IEC 60270 standard, partial discharges are “localized electrical discharges that only partially bridge the insulation between conductors and which can or cannot occur adjacent to a conductor. Partial discharges are in general a consequence of local electrical stress concentrations in the insula- tion or on the surface of the insulation."


Source: Omicron - a link to further information is given here. 

It can be said, that partial discharge results in a local breakdown. Partial discharge is a local electrical discharge that only partially bridges the insulation. 

However, through the time partial discharge will harm the insulation so strong that it might lead to a total breakdown.

Picture:
A partial discharge within solid insulation. When a spark jumps the gap within the gas-filled void, a small current flows in the conductors, attenuated by the voltage divider network Cx, Cy, Cz in parallel with the bulk capacitance Cb

 Source-Wikipedia