A connotative meaning is one that is implied by, and additional to the exact meaning of a word or phrase. For instance, if I say that someone is overweight, the exact meaning is that he weighs more than he should. That word does not have a clear connotation. If I say that someone is fat then that word has the connotation that he is unattractive and remarkably overweight.
A figurative meaning is one that covers exaggerations like: "He's as big as a house," or "He must weigh a ton."