What is a "PARTIAL DISCHARGE" in a Transformer ? What is the meaning of winding movement in a transformer and how Partial discharge test detects it ?

PD is an electrical discharge that only partially bridges the insulation between conductors. A transient gaseous ionization occurs in an insulation system when the electric stress exceeds a critical value, and this ionization produces partial discharges.

As far as winding movement is considered i dont think so partial discharge can detect it. for winding movement SFRA and Leakage Reactance tests are used on transformer. Excitation current test can also be relative in this regard.

PD is used to check insulation defects in transformers

It is not always possible to prevent minor manufacturing fault, cavities of inhomogeneities in insulating materials. Weak point of an insulator in an electrode system under voltage, can cause local over-stressing by the electric field. This in turn can lead to extremely rapidly progressing local electrical discharge, i.e. electric "Partial Discharge" (PD).
PD is generally referred to as a discharge process in which the distance between two electrodes is only partly bridged, i.e. in the cause of partial disruption of insulation. Partial discharge can originate directly at one of the electrodes or occur without electrodes in a cavity inside dielectric materials.