What does apparent and absolute motion mean in astronomy?

What appears as movement to observer is apparent motion. Any apparent motion is with reference to a moving frame. Absolute frame for absolute motion in astronomy is still a mirage.

As an observer we see Moon, other planets, our star Sun and other stars moving, at different speeds. This is apparent motion. The frame of reference is a frame, at your position, with directions that appear to be fixed in your view. This is observer-centric apparent motion. Likewise, there are Earth-centric, Sun-centric Milky Way-centric, ... apparent motions.

The fitting of absolute frame of reference for absolute motion, for continuous marking of of the space vacated by everything (relatively), at any instant, is still at large. .