In the past, barber shops were referred as tonsil parlors. OK then, what is a tonsil?

tonsorial - of or relating to barbers and barbering; "tonsorial work"; "tonsorial parlor"
http://www.thefreedictionary.com/tonsorial

Tonsure is the practice of some Christian churches, mystics, Buddhist novices and monks, and some Hindu temples of cutting the hair from the scalp of clerics, devotees, or holy people as a symbol of their renunciation of worldly fashion and esteem.
https://en.wikipedia.org/wiki/Tonsure

See above link for a drawing of a tonsure.

History shows that the barbers were also the dentists of the town. Therego, if you had to have your tonsil removed...you went to the barber. Wouldn't suggest it for present day operations.