What is impromptu dialogue?
Impromptu means done without a script or rehearsal. I would assume that for your question, impromptu dialogue would be the same as impromptu speech, but possibly with a give-and-take with the audience.
Impromptu speaking is conversation or speech that has not been rehearsed or scripted. It requires a great deal of skill and knowledge to successfully deliver impromptu dialogue. The fact that a speech or exchange is to be done impromptu does not mean that preparation is not necessary. Quite the opposite is true. A forum discussion is a great example of impromptu dialogue and it is somewhat nerve wracking because you do not know what questions or discourse will take place. For this reason, much research, preparation, and acquisition of buzzwords is necessary.