I went looking for information about this issue, but the vast majority of the stuff I found was anti-Catholic–or at best, not Catholic. I finally found
this. It’s
Commonly Asked Vocation Questions page from the Franciscan Sisters in Steubenville, Ohio.
The answer to the first question: “What is a sister or a nun?” deals with the issue of being a 'Bride of Christ."
It is not a marriage in the way that Latter-day Saints think of marriage, by any means. The wedding dress and the ring are more, from what I can see, a symbol of what nuns and sisters give UP, in return for something they feel is much better; they promise to sacrifice all of their lives, faith and efforts to their vocation, and are ‘married’ to Christ in the sense that they don’t have time for being married to anybody else.
I’m certain, however, that a Catholic can explain it much better than I can…but I found the idea a richly symbolic idea; as Latter-day Saints consider marriage and family to be our first priority (absent only our faith in God) a nun who becomes a ‘Bride of Christ’ subsumes everything to her faith. It’s appropriate symbology, I think.