en·gage·ment / enˈgājmənt/ • n. 1. a formal agreement to get married. ∎ the duration of such an agreement: a good long engagement to give you time to be sure. 2. an arrangement to do something or go somewhere at a fixed time: a dinner engagement. ∎ a period of paid employment. 3. the action of engaging or being engaged: Britain's continued engagement in open trading. 4. a fight or battle between armed forces.
J. A. Cannon
A binding, pledging, or coming together. A mutual pact, contract, or agreement.
An engagement to marry is a bilateral contract between two people whereby they mutually promise to marry one another. Formerly, a breach of the engagement to marry was a cause of action in several jurisdictions, but this is not true today.
An engagement letter is a clear delineation of an agreement that covers a particular project or employment. An attorney can require a client to sign such a letter to indicate that the person has been employed to perform specifically designated tasks.