I'd like (well, need) to be able to somehow make it so that when a user signs up for my free webhost, their account is automatically populated - ie.

- User signs up
- A directory called /admin is copied into their account, with content in.

I've heard of something called skel-dir or something, but Google didn't return anything useful, so I'm wondering if there's a script that can automatically do this for me.

are you using cPanel? If I remember correctly, you are.
In WHM under account functions there is an option called "Skelaton Directory", clicking on this will tell you where the skelaton directory is currently located and how to use it. It's typically located at /root/cpanel3-skel

This directory is what will be used as a skeleton for new accounts. For example if you place an index.html file in /root/cpanel3-skel/public_html, and then setup a new account, that account will have a copy of your index.html in their public_html directory.