Among the new features in Joomla 1.0.11 was a warning that displayed on the Global Configuration page. Its also one of the most common things we are asked about.
The main issue is security. When you're running a PHP script you need to know where your variables are coming from. If you turn registerglobals off this prevents users to your site from inputing their own variables. By doing this they can override your password variables and login to the restricted areas of your site.
By turning registerglobals OFF you can ensure that your script is in charge and not the hacker visiting your site.
More information is available here: