It comes from Alice in Wonderland.
This is what Wikipedia has to say about it:
"The Mock Turtle speaks of a Drawling-master, "an old conger eel," that used to come once a week to teach "Drawling, Stretching, and Fainting in Coils." This is a reference to the art critic John Ruskin, who came once a week to the Liddell house to teach the children drawing, sketching, and painting in oils."
So I don't think it really means anything.