A more thorough explanation:

Desponsation is an old-fashioned word that means the act of getting engaged or agreeing to get married. It is the process of making a formal commitment to marry someone.

• When John proposed to Mary, they had a desponsation ceremony to make their engagement official.
• The desponsation between the two families was a grand affair, with lots of food and music.

These examples show how desponsation was a formal agreement to get married. It was often celebrated with a ceremony or party to mark the occasion.