I remember posting after the Iowa caucuses that Obama was going to win the primary, and I think the reasons I cited then are the same ones that won the nomination for him... and it isn't the black vote. That's the most visible and handy target, but the truth is that black populations don't exceed 30% in any state, and the top black voter turnouts were only about 35%, so even on his best days, the black vote for Obama only amounted to about 10% of the voting populace as a whole. There were a whole lot of non-black voters making up the rest of the margins.
The biggest reason that Obama has done so well is that he has an inclusive view of things. Everything he says is phrased in inclusive terms... we're, ours, us, we, etc. When you listen to Obama speak, he says that "we" can fix problems, that "we're" going to change things, etc. And people respond to that message by injecting themselves into the process. They feel like they are a member of a team, and even if Obama can't do something on his own, at least he can work with someone who can. Hillary is always exclusive. With her it's always "I will bring about change" or "I will fix things". That forces the listener to think can she do it? And if the listener feels she can't, she loses their support.
The second biggest reason Obama won is that he has consistently run a campaign that is forward-focused. He always acknowledged the problems, then said that working together we can fix them. He didn't waste a lot of his time blamestorming the issues... he ackowledged them and committed to working to get them fixed. Hillary was always running against George Bush. Where Obama would say "we know the economy is in trouble, but working together with Republicans and Independents, we can get it back to where it needs to be", Hillary would be saying "George Bush ruined our economy. Our economy is a shambles because of George Bush. We don't need another four years of Bush's economic policies!" Now, which argument sounds better? The guy who's talking about fixing the problems, or the gal who's campaigning against a guy who isn't even running?