This paper offers a dialogue theory of explanation. A successful explanation is defined as a transfer of understanding in a dialogue system in which a questioner and a respondent take part. The questioner asks a special sort of why-question that asks for understanding of something and the respondent provides a reply that transfers understanding to the questioner. The theory is drawn from recent work on explanation in artificial intelligence (AI), especially in expert systems, but applies to scientific, legal and everyday (...) conversational explanations. (shrink)