The Social Graph API is Google's attempt to prise open the social network itself. Basically, for some time now there has been a de facto standard for declaring relationships on the Web. (A couple of them, actually.) It's not well-known, but there are some extra tags that you can toss into your HTML to declare your relationships to other people -- that they are friends, relatives, and so on. Hitherto, that's mostly been a toy, because you haven't been able to do much useful with it.
But now, Google has thrown its weight and crawlers behind the data. This makes lots of sense: they are crawling the whole Web and organizing its data anyway, so they might as well organize this while they are at it. So by using the new API, you can make use of that -- applications can examine the relationships that you've publically declared, and make use of those. This is in contrast to locked-down sites like Facebook and MySpace, while are leery of sharing those relationships. They have no motivation to share the data: it's their bread and butter. But as the end user, you're probably better off not having it trapped on one site.
I expect it to take a while for things to percolate through: not many people are using the social standards yet, because there was no reason to. But now, there is a powerful motivation -- it means that your social graph stops being the property of a single site, and instead simply becomes part of the atmosphere of information around you. Lots of sites can make use of the same information, and operate more sensibly in this increasingly social environment. Even more usefully, it means that you stop needing to re-declare your network for each site: there is instead a single network, that everybody is making use of.
Mind, I'm sure there will be downsides. This is *powerful* new information out in the ether, and it's going to take some time to even begin to understand the privacy implications. You don't necessarily *want* all your relationships to be public, and the Google API can only deal with public data. I'd bet that there will eventually grow some social-information providers that are more nuanced: that know about particular relationships, but only release that information to designated applications.
And the identity-management issues are going to be very hairy. OpenSocial plus the Social Graph are 2/3 of the overall equation: they answer "What can you do?" and "Who do you know?", but not the all-important "Who *are* you?". It's not obvious how to hook the Social Graph to OpenID and WS-Identity, and until that loop gets closed it's going to still be difficult to do everything you want to with this data. (Not to mention the trick of maintaining multiple separate identities online -- with automated tools doing the work, that's actually going to be trickier than it is now.)
But I suspect that this is going to be a long-term boon to everyone on the Web. Within a few years, after the remaining pieces get filled in, I expect many sites (including CommYou) to be operating with this public relationship information, and users will be able to focus on managing a single global relationship graph, instead of many duplicate copies on different sites. The social graph will be every bit as much a part of the infrastructure as the Web itself is, and everything else will run on top of it. That's exciting -- and, as is usually the case with exciting new technology, a bit scary...