For years the ed tech community has speculated about Google entering the LMS market, including Wave (discontinued, but some key features embedded in other tools), Apps for Education, and even incorrectly with Pearson OpenClass. Each time there is some possibilities, but Google has not shown interest in fully replacing LMS functionality.
Google Classroom, announced in May and with new details coming out this week, is the closest that Google has come to fully providing an LMS. The focus is much more on K-12 than on higher education.
For background on the concept, see this video from May which emphasizes roster integration (with some instructor setup required), document sharing through Google Drive, server and security through the cloud, discussions tied to assignments, and a focus on 'letting teachers and students teach or learn their way'.
Yesterday Google shared a new video that directly shows the user interface and some key features.
You can see more directly how to create a class, add students, creating assignments, sharing resources (GDrive, YouTube, website), student editing in G Docs, tracking student submissions, grading individual assignments.
What I don't see (and admittedly this is based on short videos) is a full gradebook. The grades are tied to each assignment, but they do not show any collection of grades into a course-based gradebook.
Teachers with early access to Google Classroom are starting to upload videos with their reviews. Dan Leighton has one from a UK perspective that has more details, including his concern that the system has a 'sage on the stage' design assumption.
I am not one to look at Google's moves as the end of the LMS or a complete shift in the market (at least in the short term), but I do think Classroom is significant and worth watching. I suspect this will have a bigger impact on individual faculty adoption in higher ed or as a secondary LMS than it will on official institutional adoption, at least for the next 2 - 3 years.