The answer to the big question behind the mere existence of FaceBook is as simple as the question itself: Why not FaceBook? Like every other popular invention, FaceBook met a need in a way that worked for the majority of its potential users, and at a low enough cost to make it preferrable to other alternatives.
Now, by "cost," I don't mean "how much money you have to pay to use it," because then you could argue for any other free social network as well; what I mean is "what you have to give up in order to use it."
There were many alternatives at the time and predecessors who paved the way, but each one had a particular cost (the most common being how to get your existing friends on it). I'm only 27, but I remember the days of newsgroups. These were the original message board: messages were threaded, stored on a server somewhere, and sent out in email-style format. The only problem was, when you joined a new group (For me that was alt.music.weird-al), you had to download all of the existing messages as far back as they were stored, probably 30 days or something. Then you had to keep up with it. Still, it provided a common meeting ground for people of similar interest in spite of distance.
AOL and other groups had chatrooms that offered the same type of thing in real time. AOL's benefit was that it had a large network of people already signed up as users; other companies had to go out of their way to attract them, and quite often some intermediary group would have a chatroom in hopes of drumming up support for themselves. The cost for the user was hoping you could sign in when friends were online, and that friends would be on there at all; many chatrooms sat unused while two or three people who didn't want to talk to each other idled and did other things on the internet. The cost for the business, of course, was the hassle of keeping up with it: I'm a business owner, I don't care about moderating a chatroom that will essentially turn into a schoolyard cyberbullying fest without my supervision, so i'm just shutting it down.
IRC was a popular chat program that had everything for chatting built into it, with networked servers for permitting chat. These were programmable and easier to moderate, as well as to offer differing levels of moderaters (in one room vs. across the network); the problem here was the stigma of downloading the program, which seemed kind of geeky to the outside world. Most of the channels (chatrooms) were based on porn, and the servers got out of sync quite often, but it was kinda neat how you could create a chatroom out of thin air simply by typing in the name of a unique room.
Instant Messaging programs such as AIM, YM, ICQ et al offered the opportunity to connect, but very little chance of connecting with people you've never met before. IM programs required other networks (including real-life networks) to survive. Also, you'd end up like I did with 130 friends on my list, 30 of them online all of the time but never around, and two I might actually care to talk to.
Blogging communities such as LiveJournal and Xanga help users to center attention on themselves, add new content as often as they see fit, maintain a profile page for whatever information they feel like sharing, and communicate with other writers to discuss what they have written. The only problem is, having a blog is like having a kid: fun at first, but you have to keep feeding it to keep it going. With blogging, you're expected to flesh out a complete thought, which means lots of writing; many people are turned off by that much effort, so only serious writers (or people who just really like to talk) are driven by a blog-based community. There are probably tens of thousands of blogs that never even had a single post and possibly millions that stand there as a testament to the last time their owner felt like blogging six months to ten years ago.
Eventually, social networks like Friendster, MySpace, and FaceBook began to pop up, and social popularity was the driving force behind getting people to join. I never joined Friendster, so I can't really talk about it; FaceBook I joined in 2005 and stuck with the longest; and MySpace I joined 18 months later for the simple reason of getting my music out, and I ditched it when I didn't care about something I wasn't going to update. MySpace had annoying layouts, the "bulletins" became mostly surveys about the last 10 movies you watched or the last 10 people who posted on your profile, and the profiles tended to slow down your computer as all the java crap and music took time for your browser to load.
But FaceBook emerged, and for once it was cool to talk in public about something you were doing online. Now, I could talk about all that Mark Zuckerberg did for FaceBook, but there are plenty of other writers and a movie coming out, so I won't plow somebody else's field here. What I will say is that FaceBook became popular with the college crowd first, which is generally a respected crowd for most Americans. Even if Clem from Toad Suck, Arkansas doesn't care for Harvard folks, he may know someone who went to University of Arkansas and probably has friends from high school at the nearest community college or a small state school like Univeristy of Central Arkansas. FaceBook started at the better schools and quickly trickled its way down to the smaller schools, gaining momentum as it went.
Also, FaceBook had a good look to it. Although the interface has changed over the years, the color scheme has always been white and blue, you know the font will be readable when you go to someone's profile, and you know how to find any necessary personal information on a person's page.
Lastly, Zuckerberg committed to keep changing and updating FaceBook. I can't tell you all the times over the past 5.5 years I've heard people say they hate the most recent layout, but you can't fault him for taking what doesn't work and making it work. Looking back, everything is in a much neater package than it used to be: notifications showing up on your home page instead of having to be emailed to you; a live feed to keep you abreast of things happening with your friends; integration of similar features of just about every other failed social network on the planet.
It is the successful, convenient meeting of all of these needs that helped put FaceBook where it is today. Where will it go next? Who knows. I've been saying for the past two years that 2010 would be the end of FaceBook; I know it's the end for me today, even if the rest of the world doesn't catch on for awhile (and they won't), but I don't want to be one who says "I'll go when everyone else does," because that's how I and many of you got on it in the first place - even people who only signed up this year.
So what are the costs of FaceBook? Stay tuned.