The simple answer:
Enabling file sharing allows certain files on your computer to be shared. You can choose whether or not to require username/password before people can access those files.
No one on the internet side of your router will be able to access your files unless your computer is hacked into. If you are mostly doing only web surfing you should be safe. Once you get into bittorrent or P2P networks it exposes you a little more.
Make sure you have a password set on the administrative account, otherwise anyone on your local network could access *all* the files on your computer.