As opposed to denotation or the "dictionary" literal meaning of a word, its connotation refers to the sum total of all the associations the particular word in question conjures up. The connection may be even subliminal, but it is all the more powerful because it touches the subconscious mind off guard.
One recurring leit motif throughout the novel which is multiple in interpretation is the colour green. It can mean 'without experience' (as Nick Carraway, the 'greenhorn' out East), youth, growth, lust for money, jealousy or sexual decadence. Each one of these interpretations comes to the fore at least once, if not more. The following reference goes into detail concerning this aspect of the novel.
A connotation is a suggestive meaning or an association of a word.
Look at Daisy's quote:
"All right... I'm glad it's a girl. And I hope she'll be a fool--that's the best thing a girl can be in this world, a beautiful little fool."
Originally, a fool was a male court jester (with the conical cap and bells). Later, a fool became any person lacking in judgment. Here, Daisy associates her unborn little girl with the word. Typically, the word "fool" is reserved for adults, not children, babies, or fetuses. She is obviously referring to herself as well.
Also, look at the clothing and color connotations in the novel. Look beyond their literal meanings at the way Fitzgerald is associating them with people, emotions, and social values.
Look at Nick's soliloquies. He tries really hard to make it seem he's "honest," but he's saying he is "honest" in relation to all the liars he's met. Does that really make him "honest"?
"Everyone suspects himself of at least one of the cardinal virtues, and this is mine: I am one of the few honest people that I have ever known."
If he's an "honest" person, and if he's been taught to reserve moral judgment, then why is he hanging around a bunch of "dishonest" people and judging them throughout his narration? The connotation of "honesty" is in relation to "dishonesty," so Fitzgerald is blurring its meaning.