Implicature

Something that is implied by a speaker uttering a sentence, without being part of the truth-conditional content of that sentence. The notion was introduced by the philosopher H.P. Grice to explain how speakers can mean more with their utterance than what they say. Some implicatures where conventionally tied to specific words (like but, differing from and in its conventional implicature of contrast), others follow on the basis of the Cooperative Principle and its maxims. A well-known example are the scalar implicatures, where a weaker term on a scale implicates the negation of a stronger term.

Example
(i)	John ate some of the chocolates scalar implicature : John did not eat all of the chocolates

Some includes the meaning of all, but, given the Maxim of Quantity, the speaker will only use some if he is not in a position to use all. Hence, his use of some implicates that there were chocolates not eaten by John. Notice that an implicature can be cancelled, when the speaker explicitly strengthens his utterance:

(ii)	John ate some of the chocolates, in fact, he ate all of the chocolates

Scalar implicatures are an instance of generalized implicatures (that normally follow from the utterance), in distinction to particularized implicatures (that one follows in special contexts).

Link
Utrecht Lexicon of Linguistics