1. be very occupied with something, or keep someone occupied
Professional
Social
tied up with work/meetings
If you are 'tied up' you are literally bound by rope and unable to move. The adjective 'tied up' means to be busy or occupied with a task so that you are unable to do something else. This is a popular adjective and a polite way to say you are too busy to do something or to decline an offer to do something.