Since at least medieval times, the verb “to wax” has meant “to grow,” while the opposite term, “to wane,” has meant “to decrease.” “Wax and wane” have largely fallen out of favor, except when they pop up in expressions such as “waxing poetic.” “Poetic” means just that: to speak or write in a poetic, flowery or romantic manner, and often with enthusiasm. So if your instructor asks whether “William Faulkner is waxing poetic,” she's questioning whether the author is writing in an increasingly poetic manner.
Apply the same lesson to terms such as “wax eloquent” and “wax nostalgic,” two other somewhat obscure expressions that surface from time to time. A writer who expresses himself in either way is growing more eloquent or nostalgic.