The connotative meaning of a word refers to the feeling that a word invokes. This differs from its dictionary definition, which is called its "denotative" meaning. Two words can have similar denotations but very different connotations.
For example, the words "miserly" and "thrifty" are both adjectives that describe a person who goes to certain lengths to save money. However, "miserly" has strong negative connotations, while "thrifty" evokes positive feelings in a reader. Ebenezer Scrooge, the protagonist of Charles Dickens "A Christmas Carol," is an extremely unpleasant individual who creates misery for himself and others through his penny-pinching ways. Therefore, applying the positive "thrifty" to him would be a mistake; "miserly" is much more appropriate. In this situation, choosing a definition with the wrong connotation would create the impression that a writer has somehow misunderstood a major character trait.