I realize this question is old, but the accepted answer does not really answer the question.
Is that some kind of short-hand? Maybe it's something that's built in my browser (Chrome 14)?
Yes, it's a short-hand for whichever protocol the document was served over. It avoids the dreaded "This page contains both secure and nonsecure items. Do you want to display the nonsecure items?" message.
Is it safe to use double-slash instead of http and https?
Yes, all major browsers today support it.
It's generally useless against your own site, but can be very helpful for including resources from other sites (where absolute URL's are needed) but not having to worry about HTTP/HTTPS mix-mode.
It's also helpful if your document is served from both secure and nonsecure locations, like a dev site and production site.
For details, see http://www.paulirish.com/2010/the-protocol-relative-url/