When two people are engaged, they make a mutual promise to marry each other. In some cultures, this is done in front of witnesses and may be followed by an engagement party. Being engaged carries no legal weight in most jurisdictions, but in some places, it may give the couple certain rights and obligations.
In common law countries, an engagement generally gives rise to a rebuttable presumption of intention to marry. This means that if one of the parties breaks off the engagement, they may have to prove to a court that there was no intention to marry all along. This can be difficult to do if the couple has been living together or engaging in other behaviors that suggest marriage intentions (such as sharing finances).
In some civil law jurisdictions, engagements are legally binding agreements between couples that establish certain rights and obligations towards each other. These rights and obligations vary from country to country, but often include things like alimony payments in case of divorce or annulment. Breaking off an engagement in a civil law jurisdiction can often lead to lawsuits and financial penalties for the party who backed out.
So while being engaged does not mean much from a legal standpoint in most places, there are some exceptions where it can have significant legal implications. If you're considering getting engaged, it's important to understand the laws in your jurisdiction so you know what you're getting into!