1.having ones attention or mind or energy engaged;
she keeps herself fully occupied with volunteer activities
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
5.(used of toothed parts or gears) interlocked and interacting;
the gears are engaged
6.having services contracted for;
the carpenter engaged (or employed) for the job is sick
7.built against or attached to a wall;
engaged columns
8.pledged to be married;
the engaged couple