Engagement

Engagement can mean:

1. A promise made by two people to marry, before becoming husband and wife at their marriage.
2. Having a job to perform work, or possibly music or other entertainment. (This is sometimes called a "gig".)
3. To take part or be busy in something.

Marriage

An engagement is an agreement or promise to marry, and also refers to the time between proposal and marriage. During this time, a couple is said to be affianced, engaged to be married, or simply engaged. An engagement can be seen by witnesses to confirm their marriage

A fiance is the man a woman is engaged with. A fiancee is the woman a man is engaged with.

Work

A work engagement is being hired to perform a job, usually a brief or single-event one, such as a party or public event. A performance engagement or "gig" usually means a single-event entertainment job, such as musician, clown, dancer or other performance. (A "running engagement" is a steady job of this kind.)