Engagement (noun)

1. A formal agreement to marry.
2. A commitment or promise to do something.
3. A period of time for which a professional, such as a performer or speaker, has been contracted.

Origin:

From middle english engagemen, from old french engagemant, from engager ("to pledge, commit").

Examples:

1. They announced their engagement.
2. He broke his engagement with her.
3. The company made an engagement with the client.
4. She has an engagement for a concert next week.
5. The engagement of the troops lasted for six months.