It describes how wearing military clothing as a civilian, and particularly medals and awards, can be distressing for veterans. The assumption is that people wear the clothing in order to give the impression of being tough, having endured hazardous circumstances - even specifically having served - in order to gain respect and other benefits. Hence, stealing valour.
This is stupid. If you don't wear any of the patches or medals, no sane person will accuse you of stolen valor. Nobody gives a shit if you're wearing old BDUs or ACUs.