Well, every Unix like operating system make use of what is called “runlevels”. These are numbered from 0 to 6 (actually there are more, but these are the usual and documented ones). When you restart your computer you just tell your system to enter runlevel 6. When you shutdown the computer you simply tell the system to enter runlevel 0.
Unix is a multiuser system, meaning that more than one users can be logged into the same system at the same time. By telling your linux box to enter runlevel 1 (by issuing init 1) you make your system to enter a special mode that is supposed to be used by your root account and only, and it is for maintenance purposes. This is the single user mode. To make it more clear to you, suppose that you need to clean-up your file system. In that case only the root user that runs the clean-up process must be logged in. Any other user must be forbidden to login, because that would launch processes that would create and manipulate files.
Now, when your system enters runlevel 5, it enters a multiuser mode (many users can be logged in the same system) using a graphical environment. This is the runlevel your system enters when boot-up. If you enter runlevel 3, the system still provides the multiuser ability but without graphical environment. Only the terminals are available.
You can see that if you enter just the number 3 in the kernel parameters to be passed on your GRUB screen. The result would be just a login prompt in a terminal after booting and no graphical environment or login screen;). Then if you login as root, you can issue the command init 5 and then you will see the graphical environment (the graphical login screen).
When you want to install a graphics driver, no graphical environment is allowed (imagine that is something like driving a car while you have your tires changed!..:P). So you have to enter runlevel 3 first. This will drop your graphical environment so it is better to logout from it first. If you press the keys CTRL+ALT+F1 your screen will turn to a terminal. Then you login as root and enter the command init 3. After that you can install your new graphics driver freely, without problems. When finish you can enter init 5 to launch the graphical environment again and test the new settings.
I hope this made the init thing more clear to you.