It's like.... well, I can't describe it, since I've never had anything other than 2 parents. I suppose it's sort of like.... well, you love your parent right? Well, uh, imagine having another person like that. It makes the house livelier, and it gives you an additional source of experience, morality and interaction. There are things my mother knows that my father doesn't (like how to cook healthy food, how to maintain a household, how to manage accounts) and there are things my father knows that my mother doesn't (how to cook extremely tasty yet unhealthy food and a lot of history and plant biology).
My parents interact with each other has any couple of parents do. They've been married for 30 years now. It wasn't always easy keeping the marriage afloat, but they did it and it's been very stable for the past 15 years or so. Two parents could also "combine forces" to discipline/educate a child. My father and mother had a whole bag of psychological tricks and routines to make me eat vegetables, do my homework - sort of a "good-cop/bad-cop" routine. My mother would go in with the fire and brimstone, and my father would then say some encouraging or sympathetic words, and usually he'd act as a mediator between me, my siblings and my mother (who was a very strict disciplinarian. On the other hand, her method of raising us worked. None of her children dropped out of university, did drugs or have been arrested).
Having two parents also meant that there was always someone there for us. In many single parent households, the single parent must work to provide food. In my household, my mother stayed at home and looked after us and talked to us and interacted with us. This was incredibly important - she made sure that she talked to us for hours. Played with us, taught us, made sure we did the right thing. It helped enormously.
I suppose that's the only real difference: constant interaction. Also, I now have the "tools" to manage a marriage if I ever get married. Talking to my father (who is a virtual pacifist who never, ever raises his voice above normal speaking level) has allowed me to realize that having a successful marriage means having patience, flexibility and a healthy dose of realism whenever you begin a relationship. He taught me that if you go into a marriage with fuzzy-wuzzy, holly-wood constructed notions of what "real" romance and relationships should be like, you are almost destined to get divorced. He taught me to never, ever hit your wife, to always have tolerance, respect, and to carefully think about what you say and the tone in which you say it. His marriage has been going on for a successful 30 years, so he'd know a thing or two about keeping a marriage going.