What exactly does this mean? I just boot up my computer and off she goes. No logging in required. How do you log in as root? Are there some special maintenance tasks you can do when logging in this way?
Logging in as root, means you log in as superuser, meaning you wield the power to destroy your computer easily. When you boot up your computer, it boots up in multi-user mode, which means multiple users can use your machine. (Which do, but most of the "users" are users the computer makes to do various operations with out root access eg. wheel)
If you start your computer by holding the command key and s, you start up in single user mode, meaning you are root, this is usually used for diagnostic purposes and running fsck -y. No need to log in as root that way.
The other ways of doing root commands are to enable root using the NetInfo Manager (And under the security menu, enable the root user, and if your user isn't set to auto login, at the login screen you can click on Other User... and enter root and the password). This is not as advisable as say only using root only when needed as root priveleges shouldn't be messed with unless they need to.
sudo, this stands for SuperUser DO. This is Mac OS X's way of allowing administrators of a computer do root operations while logged in as themselves, so if you ever need root access to do something, use sudo instead. It tends to be safer (except when used incorrectly). As for any special maintenance tasks, just use Cocktail, its easier, and no need to log in as root and the special risks that accompany it. SuperUser is like god, don't misuse it.