What is the meaning of Engaged?

simple past and past participle of engage

Having agreed to marry a particular person (one's fiancé or fiancée) or each other.

Busy or employed.

Greatly interested.

Already involved in a telephone call when a third party calls.

attached to a wall or sunk into it halfway

in contact and in operation

being attacked or attacking

Having the widest part of its presenting part, usually the head, enter the pelvic brim or inlet.

Synonym of engagé (passionately committed to a cause)

Source: wiktionary.org