Offline time is how long your staff will keep on earning Cash for you while you're away. You have 1 hour of offline time as standard - so if you are away for the game for 2 hours, when you come back you will only be able to collect earnings for one of those hours.

You can also purchase permanent increases to your offline time in the in-game shop:

Working Student: gives you +1 Hour Offline Time
Office Intern: gives you +3 Hours Offline Time
Restaurant Manager: gives you +6 Hours Offline Time
Restaurant Director: gives you +10 Hours Offline Time

All of these stack together with your free 1 Hour Offline Time, so for example if you buy all of them then you have a total of 21 Hours Offline Time!