Over at Google.com/posts, Google has a landing page for this feature, calling it "an experimental new podium on Google" that allows you to "hear directly from the US presidential candidates in real time on Google." It's a believable explanation until you see this Google Posts profile from "Andrew Jewelers" in Buffalo, New York, (spotted by Mike Blumenthal), which is definitely not a presidential candidate.
The landing page says the "experimental" feature is "only available to the 2016 US presidential candidates" (Andrew Jewelers for president!), but those of us not running for office can join a waitlist as Google plans to "make it available to other prominent figures and organizations."
It really seems like this is a Google+ reboot just for brands. The design definitely seems like Google+ with the Google+ branding stripped out, but this "social network" explicitly dodges being "social" AND any kind of "networking." Comments are gone, and you can't search for brands that have Google Posts or follow them. What's left is creating a profile, writing posts, and sharing pictures and video, and these posts will only be visible to people if they search for something relevant in Google.
So far we've seen posts show up in either a horizontal carousel in the middle of search results, like for the query "engagement rings buffalo," or collapsed in an answer box, like in the search "Hillary issues." While Andrew Jewelers has a profile page that is linked to its profile picture, Hillary Clinton does not. All the posts have an "On Google" label and a blue "verified" checkmark, suggesting that they are directly from the subject.
While it does seem exactly like a social network, embedding posts from a real social network into the search results wouldn't accomplish the same thing. The hyper-realtime information from social posts isn't necessarily the most important thing to show search users. In Google's presidential candidate example, for instance, it's much better to show information, like their stance on issues—information that is probably months old—rather than something from Twitter, which would probably be what they had for lunch.
A good example of how this is useful is in the "[presidential candidate] issues" example. Donald Trump does not have Google Post entries for this query, so the answer carousel shows quotes from news articles. Clinton does have Google Post entries, so you get a direct, concise, complete statement presumably approved by the campaign. Businesses, on the other hand, seem to just be using it like a social network by showing the latest sale. We'd imagine brands like the lack of comments, meaning they can send out a message unchallenged as a sort of "one way social network."
Ultimately, Google Posts seems to be a new place for Google to directly host content. Usually it's more "evergreen" content that isn't just the latest social media post. It's aimed at "Brands"—companies, celebrities, etc—and there are no comments. The only way to see comments is to hit on a magic search result, where they'll show up directly on the results page. It's an experiment for now; we'll have to see what things look like once the waitlist starts being fulfilled