Perhaps a girl would better answer this, but I can still give my current beliefs as to why they want marriage. Women want security. They want to feel safe, and going through all the trouble of getting married and the hell it takes to get a divorce adds a greater sense of stability than something that is more easily called off with but a few words. Furthermore, saying "My husband" has more meaning than "My boyfriend," adding a kind of "proof" that he loves her if he's willing to tie the knot.
Then again, there are also women like this: