Helping people with computers... one answer at a time.
A VPN, or Virtual Private Network, allows users to remotely access a particular computer.
Corporations do this all the time. It's called a "VPN" or virtual private network, and it allows anyone on the internet, with the right user name and password, of course, to connect to a local network as if they were right on it.
I've toyed with setting one up myself, but have yet to actually done so. There are a couple of ways to go...
The approach I expect to try first myself is to use a router that provides VPN functionality. For example, you might replace your NAT router with one that also supports VPNs, and then after some configuration your brother should be able to connect to your network.
The specifics of how that gets configured is the magic part that I'm not yet familiar with.
Having used them as a client in the past, the experience works something like this: the client (your brother, in this example) would simply create a dial-up connection that uses the internet instead of a modem, and "dials" your IP address, logs in, and gets connected through your VPN router or software. While he's connected to your VPN, he can see whatever drives you care to share. He might not be able to see the rest of the internet, though.
If you're running Windows XP on both ends (and XP Pro on at least one), you can also look into Remote Desktop. The current Remote Desktop Client will allow the drive(s) to be mapped to the client machine. The downside here is that Remote Desktop will take over the console of the server while you're connected.
Practically Networked is also a good general resource, though perhaps a bit difficult to navigate.