Engagement

noun

1. An appointment, especially to speak or perform.

   "The lecturer has three speaking engagements this week."

2. Connection or attachment.

   "Check the gears for full engagement before turning the handle."

3. (by extension, about human emotional state) The feeling of being compelled, drawn in, connected to what is happening, interested in what will happen next.
4. The period of time when marriage is planned or promised.

   "We are enjoying a long engagement, but haven't yet set a date."

5. In any situation of conflict, an actual instance of active hostilities.

   "The engagement resulted in many casualties."