Definition of "Engaged" :

adjective: having ones attention or mind or energy engaged

"Deeply engaged in conversation."

adjective: built against or attached to a wall

"Engaged columns."

adjective: having services contracted for

"The carpenter engaged (or employed) for the job is sick."

adjective: (used of toothed parts or gears) interlocked and interacting

"The gears are engaged."

adjective: involved in military hostilities

"The desperately engaged ships continued the fight."

adjective: (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)

"Receptionists' telephones are always engaged."

adjective: reserved in advance