What I think the real reason for existence of Google Plus is not social media but social searching. Think of it, where do you see the Google Plus button or icon most often, on the Google Search results page.
Google has long talked about keeping its SEARCH ENGINE ahead of others. (If you remember, Google primarily started as a search engine & not the grand daddy of everything internet)
I think Google Plus is another step towards it.
Google Plus is primarily being used for one thing, +1 recommendations (similar to facebook like) which appear on the google results & can affect the results you see. & That is the only thing it is being used for, effectively. Very few websites get a lot of traffic from Google+ sharing directly, as compared to facebook sharing (stats available easily on google).
This becomes even clearer after failed social media efforts by Google in the form of Google ME & the upgraded (read degraded) Orkut. Because, as I mentioned earlier, Google+ has no remarkable feature that is not already there on facebook & it does not have as many (or even slightly close) users as facebook.
But again, this is what I think, Larry Page & Google fans can differ.
P.S. : I'd started writing this post sometime back, finally completing it today.