A betrothal is the agreement that two people will marry — the promise itself, and sometimes the little ceremony that makes the promise public. It sits before the wedding. In older Europe it could be almost as binding as marriage, and families often treated it as a contract, not only as a feeling. Today English speakers usually say engagement for the same stage of life. Betrothal sounds like a history book, a very formal church setting, or a careful word for a culture that still treats the promise as official and heavy. If you only need the ordinary school word for “we plan to marry,” engagement is the one people expect.