The tradition and the symbolic commitment of said tradition. You say to the world "I love this person enough to be legally bound to them for the rest of my life" - at least that's what you're supposed to be saying. It doesn't always work out that way, of course. It's a pledge. Sort of like the Pledge of Allegiance, even. Except to your spouse, not the country you're living in.
Marriage aside, it's good for all children to have both male and female influences in their development stages. As long as the influence is positive, anyway. My father doesn't really have any influence on my life, he's just a machine who goes to work, hates it, comes home and watches the motor sport and tells us about how shit his job is. I can't recall him doing much more than that with his life. He's a boss, not a father. I turn to The Art Of Manliness and male friends that I've made only in the last 3 years, for actual examples of man stuff. It didn't exist for me before that, because my dad isn't a father. How does marriage fit into that? Well, I guess if you commit to another human being, you commit to having children (if possible; note that children aren't always part of the plan, or wanted). I don't think marriage explicitly states that you'll commit to the children of the married couple, however. But it is implied, at least where "nuclear families" are concerned.
Of course, we live in a 'new world' where it's not expected, and those who reach their thirties without marrying aren't considered "spinsters" or "losers" or whatever.
Whether you're a "loser" for not finding anyone full stop by a certain age, is another matter.