What is peeling off my gum?

Without a picture its difficult to make a diagnosis.  The most likely possibility is that you have a minor chemical burn resulting from any number of dental materials used during the impression phase or temporary creation phase of your appointment.  This could cause the tissue around your tooth to slough (and peel).  You should call your dental office and let them know whats going on, they will likely want to take a look to be sure the area is recovering from the procedure.