Idioms: get on, be off, keep someone

Look at this short conversation.

Joe: Well, I'd better be off soon. I have a lot of work to finish...
Sue: Oh, of course. Don't let me keep you. I should be getting on myself.

These expressions, be off, keep someone and get on are casual expressions. They are often used when finishing conversations and saying goodbye.

be off and get on both mean 'leave/go'.
keep someone means 'stop someone from leaving' or 'make someone stay'. If I say 'don't let me keep you', I mean 'I know you're busy; please go if you need to go'.

He's off on another trip to London.

I'd better be off. I have to pick up my kids from school.

I don't want to keep you. I know you're busy.

Sorry to keep you all here so late, but we need to have a quick meeting.

Wow, look at the time... I must be getting on.