Besides a promise of marriage, it can also figuratively represent 'a strong promise or commitment to something'. For example, you could say, "I'm married to my job 💍".

In fandom culture, it's sometimes used when jokingly saying "let's get married" to express deep affection for a favourite celebrity. It's also cleverly used, like in Beyoncé's song, to show a strong will to 'make something precious your own'.