Imagine a group of people who were all on equal footing with each other. Somehow, they decide to get together to talk. They want to see if they can think together. They don't have any predetermined topic, or any goal of the group, other than to just talk together and communicate. Now, what happens?
Usually, they wonder what Dialogue really is, because they have never experienced it before. They try to be polite, but sooner or later something happens. Probably what happens will be uncomfortable, but if the members of the group can hang in there, something very interesting happens.
People open up and stop defending themselves. They realize they don't have anything to lose by revealing themselves. People begin to tell each other where their opinions and beliefs came from. Sometimes they realize that each of them has very unique thinking strategies and they start to investigate what these differences are and how the differences can work for all of them. They team up on a question that means something and they get very excited. The people who seem to talk too much relax and listen more often. They persuade the people who are shy to speak up more often. Sometime the group comes up with customs that help new people who might join in the middle to feel more comfortable. Sometimes people walk away still talking to each other.
(Anyway, that's a little about what Dialogue has been for me. If you have any experiences in Dialogue, please add a little about what it is for you.)