The purpose of Google+ is to keep you within the Google web (as opposed to having you outside anybody’s web, or in someone else’s web). Where “web” used to mean the spidered collection of documents and files available via HTTP, but has grown to mean your Digital Life.
Google’s business is to mediate as much of your Digital Life as it can — similar to the way Microsoft’s business in the old days was to mediate as much of your Digital Office as it could (back in the day when Digital Life and Digital Office were nearly equivalent). The monetization model is completely different, of course; but the more of your Digital Life Google can mediate, the more they can monetize, and the more sticky the whole suite is. Google wants to be as ubiquitous as Microsoft used to feel.
(Google and Microsoft have also had altruistic goals of making the world a better place while running their business, but of course that means they have to be successful at business to be successful in their altruistic goals.)
Google has been pretty good at understanding how far Digital Life will reach into Real Life. Want to find out where you are physically and where you’re going? There’s a Google (Maps) for that. Want to watch millions of channels of video? There’s a Google (YouTube) for that. Want to talk to your friends, family and business associates on the phone? There’s a Google (Android, Voice) for that. Etc.
It took them a while to figure out that “socializing with friends” was a big part of regular folks’ Real Life, and then it’s taken them a while to figure out how to make a Google for that. But it looks to me like they got it right with Plus.
Bonus look at the other players in the game:
Apple: understands the idea of a Digital Life, but hampered by its long-term view that Digital Life would be built around digital assets (documents, apps, media), instead of Real Life.
Facebook: has a huge head start on mediating your Digital Life, because it’s built on socializing, which is a big part of regular folks’ Real Life. May or may not figure out there are other parts to it.
Microsoft: mediated most people’s Digital Life for a long time. Parts of it understand that there’s more to Digital Life than Digital Office. But they may die by milking their old cash cow (Innovator’s Dilemma) before succeeding in the new game.
Yahoo: accidentally, subconsciously, understood Digital Life early on. Couldn’t wake up and realize it consciously, gave away the race.