Definition of "engagement"

(countable) An appointment, especially to speak or perform.  examples

(countable, uncountable) Connection or attachment.  examples

(uncountable, by extension, about human emotional state) The feeling of being compelled, drawn in, connected to what is happening, interested in what will happen next.  quotations  examples

(countable, uncountable) The period of time when marriage is planned or promised.  examples

(countable, uncountable) In any situation of conflict, an actual instance of active hostilities.  examples

(fencing, countable) The point at which the fencers are close enough to join blades, or to make an effective attack during an encounter.  examples