Figurative language is when you use a word or phrase that does not have its literal meaning everyday. There are a few different ways to use figurative language, including metaphors, similes, personification and hyperbole.
Connotative language is basically the use of figurative language. To say someone is "green with envy," we know that they are not really green because of envy, but we get the idea that they are really jealous of something. It is to give a connotation* to a word or phrase, alternate to its actual, literal meaning.