Prior to Classroom,
teachers would share documents with students. Often they would need to remind the students to make their own copy of the document, rename it with their student name, and then share it again with the teacher. While there were benefits to this, like teachers being able to view students work as they worked on it in real time, it was a bit of a hassle and sometimes created an organizational disaster area of the teacher's Google Drive. I think the best feature of Google Classroom is that if a teacher wants to assign students to complete a document that they have started in Google Doc or created a template for in Google Docs, they can have Google Classroom "Make a Copy for Each Student" when they create the assignment tied to that document. When this is done, each student will get to their own copy by clicking on the title of the assignment or be looking in their own Google Drive.
I could go on and on with how it works and how awesome it is, but there are a couple of well done videos that can show you all that.
Here are a couple links to pages that tell you what you can do with Google Classroom:
20 Things You Can Do With Google Classroom http://www.alicekeeler.com/teachertech/2014/09/07/20-things-you-can-do-with-google-classroom/
15 More Things You Can Do With Google Classroom
http://www.alicekeeler.com/teachertech/2014/09/22/15-more-things-you-can-do-with-google-classroom/Here is a link to another vimeo video that is well done. http://vimeo.com/101261736
If you are in need of some instructions on the use of Google Classroom, here is a link a Google Doc I created. http://bit.ly/1miFOYr