If you're in an ongoing discussion with someone over, say, the best way to train a dog, that means you talk to each other over a long period of time, about all the aspects of dog training.
Discussion comes from the Latin for "examination by taking things apart," and when you're having a discussion with someone on a complicated topic, it's like you're taking it apart and trying to understand it. Usually in a discussion, people exchange ideas. If you say, "I adore bananas," and your friend says, "me too," that's hardly a discussion. But if your friend says, "bananas are disgusting," then you can get into a discussion about it.