I don't understand the structure of the sentence.
This sentence has a literal meaning. Ellen is saying here that children always have a sticky substance on them, like food, or something they have been playing with, like paint, therefore they are in general "sticky". The structure of this sentence goes "subject" (they) "verb" (are) "sticky" (adjective). Then, "is what they are" means "that is what they are", and "that" (meaning "sticky") is implied.