In git documentation (like git-checkout-index http://linux.die.net/man/1/git-checkout-index ), there are references to "stat information" in the index file. What is this mysterious "stat information"?
That's information that would be returned by stat() - in particular, file permissions, since that's what's actually tracked. (Other information includes timestamps, filesize, user/group owners, and the inode.)
There's also a command-line program stat which is essentially a wrapper for that system call; try stat <file> and you'll see all that kind of information.