Without more context, I can't say. "We're off!" means "We're excited to be starting on a journey!" "Are we ready to leave?" "Let's do one last check. We have the tent. We have the sleeping bags. We have the camp stove. All the car doors are closed. We're ready!" "OK, fasten your seat belt. We're off!"

I think ,if its applying to a relationship between a man and a woman,it means each one of you must give space,but the relationship is not yet over.

- it means to be leave, depart - I'm just off to the bar for a few drinks - or to be free from work, school, or some other regular occupation, as in The secretary is off today, but perhaps I can find it.