Peel derives from an old verb pill, �to plunder�, which is the root of our modern word pillage. It came to us from the Latin root pilare, meaning �to take the hair off, pluck� but which also had the figurative meaning of �plunder, cheat�, almost exactly the same as the figurative meaning of our modern verbs fleece or pluck. From about the 17th century on, pill was commonly spelt peel and took on the sense of �to remove or strip� in the weakened sense of removing an outer covering, such as a fruit. The figurative sense of keeping alert, by removing any covering of the eye that might impede vision, seems to have appeared in the US about 1850.
From Worldwide Words.