an agreement between two people to marry; the period of time that two people are engaged before they marry
The couple announced their engagement on Wednesday.
an official arrangement to meet someone or do something at a particular time, especially one that is related to your work
Unfortunately I'll have to miss the meeting as I have a prior engagement.
the process of becoming involved with someone or something, especially because you want to reach a better understanding
The Trade and Industry Secretary has called for a greater public engagement with science.