having ones attention or mind or energy engaged; "she keeps herself fully occupied with volunteer activities"; "deeply engaged in conversation"
(of facilities such as telephones or lavatories) unavailable for use by anyone else or indicating unavailability; (`engaged' is a British term for a busy telephone line); "her line is busy"; "receptionists' telephones are always engaged"; "the lavatory is in use"; "kept getting a busy signal"
having services contracted for; "the carpenter engaged (or employed) for the job is sick"
busy or occupied; involved: deeply engaged in conversation.