The “Axis of Action” can be a confusing principle, and is often made more so by well-meaning explanations. The basic idea is that something on the left side of the screen should stay on the left side of the screen, even if the camera moves. It’s particularly important to maintain this relationship when shooting characters interacting. Breaking this rule is visually jarring to the audience, and usually looks like a mistake, even if a director has chosen to do it intentionally for some reason.
The “180-degree rule” is a guideline that helps maintain the axis of action. To clarify this important point, here’s a brief video I made.