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To “go on and on” is to extend for a long time. This is often used to describe something unpleasant or to describe someone talking for an extended period.
For example, if you say, “The meeting went on and on without achieving anything,” you’re complaining about how long the meeting lasted. This is something unpleasant lasting for a long time.
“He went on and on about his European vacation.” This sentence means that a person talked for an extended time about his vacation; depending on the context, it may have a slightly negative tone, but not necessarily.
It’s common to say, “I could go on and on about…” a topic. That means, “I could talk for a long time about this topic.” You could say, “I could go on and on about the differences between living in Europe and living in North America.” That means, “I could talk for a long time about this topic” or “I know a lot about this topic.” We generally say this when we mean, “I’m going to stop talking about this subject now, but I have more to say if you’re interested.”