Linux supports virtual consoles. These are a way of making your single machine seem like multiple terminals, all connected to one Linux kernel. Thankfully, using virtual consoles is one of the simplest things about Linux: there are ``hot keys'' for switching among the consoles quickly. To try it, log in to your Linux system, hold down the left key, and press (that is, the function key number 2).
You should find yourself at another login prompt. Don't panic: you are now on virtual console (VC) number 2! Log in here and do some things -- a few ls's or whatever -- to confirm that this is a real login shell. Now you can return to VC number 1, by holding down the left and pressing . Or you can move on to a third VC, in the obvious way ( - ).
Linux systems generally come with four VC's enabled by default. You can increase this all the way to eight; this should be covered in The System Adminstrator's Guide. It involves editing a file in /etc or two. However, four should be enough for most people.
Once you get used to them, VC's will probably become an indispensable tool for getting many things done at once. For example, I typically run Emacs on VC 1 (and do most of my work there), while having a communications program up on VC 3 (so I can be downloading or uploading files by modem while I work, or running jobs on remote machines), and keep a shell up on VC 2 just in case I want to run something else without tying up VC 1.