Right before I left for ISTE I was given access to Google Classroom and I have been playing with it ever since. As a teacher I mostly used Moodle as my LMS and used Google Docs, this was before I knew about Doctopus which is what I would have used if it was available then. Google Classroom has features of both an LMS and Doctopus so that teachers can easily create assignments using Google Apps and even creates an easy to manage online discussion forum. It is very easy to use and quick to set up, which also means that there is not a ton of features built into it just yet but I fully expect Google to be adding to it as time goes on.
Google Classroom will be available to all schools that have the Google Apps for Education accounts this August, a change from earlier this year when they said September. You can quickly create a class online, add students, create assignments and manage online discussions; all without students having to learn another password. It is integrated with Google Drive and YouTube, allowing you to easily create assignments and attach resources such as YouTube videos. It even allows you to create a copy of a Google Doc for each student for assignments, similar to what you can do with Doctopus but without some features that Doctopus gives you.
If anything, Google Classroom will make it easier for any teacher to get a digital learning environment created for their classroom to assist the learning taking place in the physical classroom. Watch the videos to see how it works and keep looking for your own access to it at some point. (if you go to classroom.google.com on your school GAFE account, you will either see you have access to it or not, you can always join as a student if someone else in your district has access to it)
UPDATE: Forgot to add that students can also create a file directly from the assignment area in Google Classroom that has their name and the title of the assignment automatically in the name of the file.