Meaning of “move on” - Learner’s Dictionary

move on

phrasal verb with move uk us /muːv/ verb
NEW PLACE

to leave the place where you are staying and go somewhere else:

After three days in Madrid we thought we'd move on.
NEW ACTIVITY

to start doing a new activity:

I'd done the same job for ten years and felt it was time to move on.
NEW SUBJECT

to change from one subject to another when you are talking or writing:

Let's move on to the next topic.

(Definition of “move on” from the Cambridge Learner’s Dictionary © Cambridge University Press)