Literally, to cause an unpleasant tingling of the teeth. More generally, the expression is used to describe any feeling of unpleasant distaste.

The earlier form of the phrase was ‘to edge the teeth’ and described the feeling of sensitivity caused by acidic tastes, like raw rhubarb.

A Middle English citation of a version of ‘teeth on edge’ is found in Wyclif’s Bible, or to give it its full name The Holy Bible, made from the Latin Vulgate by John Wycliffe and his followers, 1382:

“And the teeth of sones wexen on egge.”