mid-14c., "place where one lives or dwells," also "general course of actions or habits, manner of conducting oneself in the world," both senses now obsolete; from Old French conversacion "behavior, life, way of life, monastic life," and directly from Latin conversationem (nominative conversatio) "frequent use, frequent abode in a place, intercourse, conversation," noun of action from past-participle stem of conversari "to live, dwell, live with, keep company with," passive voice of conversare "to turn about, turn about with," from assimilated form of com "with, together" (see con-) + versare, frequentative of vertere "to turn" (from PIE root *wer- (2) "to turn, bend").
Sense of "informal interchange of thoughts and sentiments by spoken words" is from 1570s. Used as a synonym for "sexual intercourse" from at least late 14c., hence criminal conversation, a legal term for adultery from late 18c. Conversation-piece is from 1712 as "painting representing a group of figures arranged as if in conversation;" 1784 as "subject for conversation, something to talk about."
1640s, "relating to the art of reasoning about probabilities," from Latin dialecticus, from Greek dialektikos "of conversation, discourse," from dialektos "discourse, conversation" (see dialect). From 1813 as "of or pertaining to a dialect or dialects."
c. 1200, "literary work consisting of a conversation between two or more persons," from Old French dialoge and directly from Latin dialogus, from Greek dialogos "conversation, dialogue," related to dialogesthai "converse," from dia "across, between" (see dia-) + legein "to speak" (from PIE root *leg- (1) "to collect, gather," with derivatives meaning "to speak (to 'pick out words')").
The sense was extended by c. 1400 to "a conversation between two or more persons." The mistaken belief that it can mean only "conversation between two persons" is from confusion of dia- and di- (1); the error goes back to at least 1532, when trialogue was coined needlessly for "a conversation between three persons." And compare quadrilogue "dialogue of four speakers" (late 15c.), in the title of the English translation of "Quadrilogue invectif," which consists of an allegorical dialogue between the Three Estates and a personified France.
A word that has been used for "conversation between two persons" and cannot mean otherwise is the hybrid duologue (1864).