An antiquated and euphamistic term referring to the act of defecating in one's undergarments unintentionally, specifically when attempting to expel gas. The term would generally be used by an elderly woman.
See also; Hershey squirts, diarrhea,
Medical Doctor: "Have you been experiencing any diarrhea or other GI problems recently?”
Elderly Female Patient: “Well I do get the Panty Burps every now and then.”