Transcutaneous electrical nerve stimulation (acronym TENS) is the principle being used in the mentioned procedures. There was a big movement in the 1980's for it in dentistry, but it proved to be not as effective as advertised.
Pretty much, you overload the desired nerve trunk with an electric current so that its normal electrochemical pathway is overwhelmed and unnoticed by the body.
Very nice in those cases where it worked, well. Not so nice when it didn't.
Mrs. Lawson, I would be more than happy to participate in such an impression at an event of your choosing. However, my supplies of chloroform and ether are greatly diminished, so we may have to resort to each patient acquiring his own, personal allotment of anesthetic, in whatever form it may be found.
There are also no guarantees that said operator will be fully within his wits during said procedures, as it is a thankless job, and said operator must find solace and comfort where, and how, he can, and at whatever hour he may find it.