They do prioritize faster sites over slower sites, and they announced it at least a year ago or more, but I think we can all agree that despite Google's announcement, the mobile web is still pretty slow. (Like, average page can take 8s to load.)
Google noticed that the mobile web is still pretty slow, and they also noticed Facebook's Instant Articles initiative. Under Instant Articles, news sites provide a special RSS feed with limited HTML features to Facebook, who caches the results and shares ad revenue with the news site. As a result, viewing participating news sites in Facebook is faster than viewing them in a web browser, e.g. in Google search results.
Google saw this as a strategic threat, and said: "How can we do what Facebook's doing, making news sites provide fast lightweight HTML to Google and our users, but in a more Open way? At least somewhat more open?" AMP was the result.
When you use AMP on your site, a third party (Google--in principle anybody, but in fact just Google for the moment) can verify easily that a site will load quickly, by design. They don't have to launch a browser and run a speed index test; they know, for sure, that the page is going to be pretty fast.
A third party also knows that all AMP pages allow third parties to cache them. (Again, only Google is doing this today, but it could be anybody, e.g. Facebook could present AMP pages from a fast Facebook cache, too.)
Google takes no ad revenue from AMP pages, and supposedly doesn't rank AMP pages higher (except by virtue of the fact that AMP pages tend to be faster and faster pages rank better). AMP pages do also get the lightning-bolt badge in search results, which might encourage users to click on them. And AMP has a github and accepts actual PRs, so AMP is open in that sense, too, except that it's officially governed by Google, so it's not really very open in governance.
Folks here seem to be pretty skeptical of AMP; I think it's a mixed bag. One positive outcome of AMP would be if its HTML components eventually become official elements in a future HTML document, built into browsers. Then AMP would be nothing more than a set of guidelines and a validator; that sounds pretty good to me.