When you access a web page it is possible for the author of that page to get several items of information from your computer, unless you have installed software to prevent access. They can read your hard drive, as you have discovered, and list your folders. They can drop cookies onto your machine, read and manipulate those cookies if your browser settings allow this to happen. If someone manages to infect you with the proper virus (NIMDA for example), the virus will share your hard drive, report your IP number to the hacker, install a keyboard logger, and report your keystrokes to the hacker. What this means is that if you are hacked with a keyboard logger and type in a password or credit card number, the hacker has that information. If your hard drive is shared, then the hacker can also copy information from your drive, or can manipulate other files on your computer.
That's for starters. Web site owners can also tell where you have been on the net, which pages you left to reach their site, which pages you jump to when you leave their site. Companies that deal with cookies like doubleclick keep information in the cookies about web site visits then report this information to their subscribers (that's one way you get spam from people you never heard of).