In a grammatically correct sentence, every word MUST function as some part of speech. So, yes ... "finger-licking" is a hyphenated construction that functions as an adjective. These are not uncommon: "That was an eye-popping display of strength!" "Our end-of-year sale begins tomorrow." "The two teams will meet in a best-of-five series to decide the championship."

Yes, in this sentence 'finger-lickin' functions as an adjective. It describes the noun - the food. In the phrase 'finger-lickin' good' it is an adverb, modifying the adjective - good.

Of all you folks, really only Joe is right; 'finger-licking' really functions as an adjective; like: "A beautiful event." "An eye-catching event."

"Finger-licking" means just that: you lick your fingers, to get all the taste of the food. The full phrase is "finger-licking good" (=delicious!). I can't really imagine using "finger-licking" separate, unless you were making a joke.

Finger licking is not an adjective, its a phrase actually which simply means "excellent", specially for foods. It was originated by KFC, as its advertising slogan.