In all likelihood, most of your experiences with borders have been fairly tense affairs as serious border guards ask you questions and possibly search your belongings.
Those questions are pretty simple but they don't always feel that way when you're put on the spot and feel like a wrong answer can have serious consequences.
But while that's the gist of how it goes stateside, there are parts of Europe where you can easily cross a border without realizing it. Not only does EU membership make those borders easier to cross, but the actual division points can often be found in normal-looking streets and fields with no gates to speak of.
So while it sounds insane that one person could possibly redraw a nation's borders by accident, it's a very real possibility in the regions I just described.