Definitions of engagement:

• noun:   employment for performers or performing groups that lasts for a limited period of time
• noun:   the act of sharing in the activities of a group

  Example: "The teacher tried to increase his students' engagement in class activities"

• noun:   contact by fitting together

  Example: "The engagement of the clutch"

• noun:   the act of giving someone a job
• noun:   a mutual promise to marry
• noun:   a meeting arranged in advance
• noun:   a hostile meeting of opposing military forces in the course of a war

  Example: "He lost his romantic ideas about war when he got into a real engagement"