Conversational implicature is a concept in pragmatics, which refers to the meaning that is implied by a speaker's utterance, rather than the literal meaning of the words used.
When we communicate with others through utterances, we often make inferences based on what is said and what is left unsaid. Conversational implicature is the way in which we convey meaning beyond the literal interpretation of our words, by using indirect language, sarcasm, irony, or implying things through context or shared knowledge. The implicature is something the listener has to figure out and deduce, not something directly included in the utterance itself.
For example, if someone close to you says "we need to talk" in a certain tone, the conversational implicature is not just that a conversation is desired but that there is something wrong. The literal meaning of the words is simply a statement of need, but the tone and context of the utterance convey additional information and implications.
Understanding conversational implicature requires taking into account not only the words used, but also the speaker's intentions, the context of the conversation, and shared knowledge between the speaker and listener. It is something, for example, that learner of
new language are prone to misunderstand since they don’t know the cultural contexts
of things said and how they are being said (like misunderstanding sarcasm)