Google Sites provides discrete sites which can contain static pages, wiki-like pages, announcement pages, file cabinets, and attachments. In addition, Google Sites can integrate content from other Google Applications like Docs and Calendar, and outside sources like YouTube and RSS feeds.
It's really well suited for small to mid-size discrete research projects. You might want an "inside" site to share files or information with the team and an "outside" site to be the public presence for your project. It's also good for quickly sharing info. For example, if you were having a project review, you might set up a dedicated site for this purpose. Hey, we've got a video about doing that.
Google documents can be attached anywhere on a site without regard to size. Non-Google documents, however, have limits: 10MB for a file in a file cabinet page; 50MB for a file attached to any page. There is no size limit for the site as a whole, but the entire lbl.gov domain has a limit of approximately 5TB. (TB stands for Terabytes; 1TB is 1,000 GB.)
Berkeley Lab Resources
Classic Google Sites
Google Sites help
Embedding a Google Document in a Google Site
Video explaining concepts
Video to get you started
Google Sites User Guide
Google Sites tutorial
There's also a third party web site that seems to have some good information. The author is someone recognized by Google as a frequent contributor to the Google forum.
New Google Sites (Nov, 2016 onwards)
Websites of LBL groups that use classic Google Sites:
IT Division Help Desk: (510) 486-4357, http://help.lbl.gov