Connotation

A connotation is a commonly understood cultural or emotional association that any given word or phrase carries, in addition to its explicit or literal meaning, which is its denotation.
A connotation is frequently described as either positive or negative, with regard to its pleasing or displeasing emotional connection. For example, a stubborn person may be described as being either "strong-willed" or "pig-headed"; although these have the same literal meaning ("stubborn"), "strong-willed" connotes admiration for the level of someone's will (a positive connotation), while "pig-headed" connotes frustration in dealing with someone (a negative connotation).
Usage.
"Connotation" branches into a mixture of different meanings. These could include the contrast of a word or phrase with its primary, literal meaning (known as a denotation), with what that word or phrase specifically denotes. The connotation essentially relates to how anything may be associated with a word or phrase; for example, an implied value, judgement or feelings.
Logic.
In logic and semantics, "connotation" is roughly synonymous with "intension". Connotation is often contrasted with "denotation", which is more or less synonymous with "extension". Alternatively, the connotation of the word may be thought of as the set of all its possible referents (as opposed to merely the actual ones). A word's "denotation" is the collection of things it refers to; its connotation is what it implies about the things it is used to refer to. The connotation of dog is (something like) four-legged canine carnivore. So saying, "You are a dog" would "connote" that you were ugly or aggressive rather than literally "denoting" you as a canine.
Related terms.
It is often useful to avoid words with strong connotations (especially pejorative or disparaging ones) when striving to achieve a neutral point of view. A desire for more positive connotations, or fewer negative ones, is one of the main reasons for using euphemisms.
Semiotic closure, as defined by Terry Eagleton, concerns "a sealed world of ideological stability, which repels the disruptive, decentered forces of language in the name of an imaginary unity. Signs are ranked by a certain covert violence into rigidly hierarchical order. . . . The process of forging ‘representations’ always involves this arbitrary closing of the signifying chain, constricting the free play of the signifier to a spuriously determinate meaning which can then be received by the subject as natural and inevitable".