Apparent motion is the appearance that celestial objects move due to the motion of Earth. If all the objects that appear in the sky are moving similarly, then it is far more likely that the movement is only apparent and caused by the motion of the observer.
Flat-Earthers claim that the motion of celestial objects “proves” that Earth is stationary, and the celestial objects are moving. By the same “reasoning,” we can conclude that the train we are in is stationary, it is just all the objects outside, as luck would have it, are moving in a very similar fashion.
Flat-Earthers would say that we know the train is moving from different observations, like that we can feel the train is accelerating. However, the same thing can also be said for the motion of Earth. While the movement of celestial objects is only indirect evidence we can infer from, we can directly know the Earth is rotating from the Coriolis effect, the Eötvös effect, and gyroscopic precession. And we can directly know Earth is in motion around the Sun from observations like stellar parallax, stellar aberration, and the Doppler effect.