Ed M. answered 01/23/16
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The word dialogue--or, as it is more commonly spelled in American English, dialog--refers to a verbal exchange of thoughts or ideas between at least two parties. A synonym might be conversation (or informally, a chat), but to describe something as a dialog implies that the discussion is more substantive and purpose-driven. And because you identify your context with the tags "Teaching Speaking" and "Teachers [sic] Training," maybe the word has a specific educational sense and usage also that I'm not aware of, if it's not meant to refer to discussions in a class between or among a teacher and students or an audience.
And impromptu means 'unplanned' or 'unscripted', so I'm assuming an impromptu dialog(ue) is a conversation that is begun without specific prior intent and/or that does not have any predetermined structure or content. A synonym for impromptu in this latter meaning might be free.