Old Latin, for some people, gives an air of sophistication and authenticity to proceedings - especially for marriage vows in a wedding ceremony. But be careful not to get carried away.
By far the most important part of a wedding ceremony is the exchange of vows. The wisdom of exchanging vows in a language that your invited witnesses do not comprehend, is something that should be considered very carefully. Latin has no benefit over words that you, your partner, your families and friends, can understand. The sincerity of the vows does not increase with exoticness; quite the opposite.
literal translation
Priest:
Groom:
Priest:
Bride:
In today's Catholic Church, if Latin vows are used, they are usually followed by standard vows in contemporary English that the congregation can understand.