1. having ones attention or mind or energy engaged;
"she keeps herself fully occupied with volunteer activities"
"deeply engaged in conversation"
2. involved in military hostilities;
"the desperately engaged ships continued the fight"
3. reserved in advance
4. (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"
5. (used of toothed parts or gears) interlocked and interacting;
"the gears are engaged"
"meshed gears"
"intermeshed twin rotors"
6. having services contracted for;
"the carpenter engaged (or employed) for the job is sick"