You've already been using the Internet to make all kinds of connections to other computers. Telnet is another way to connect, but telnet is for making a direct connection to the computer.
Telneting to a computer will allow you to give it commands directly, but in order for this to work, you should have access to an account that you are allowed to use. Sometimes people set up generic login names for users that are available to the public, like guest or newuser. Sometimes the telnet session is set up so that you don't have to type a username or password.
The best way to see this in action is to try out a telnet session. Your web browser must be configured properly to access a local telnet program. Otherwise, pick up a telnet program for Windows or NCSATelnet for the Mac. When you start the program, it will ask you for a host. If you were logging into Internet Direct, type www.direct.ca. Then the host will ask you for a login name and passsword. If you are registered, and have an account, you will be able to log in, see the UNIX prompt, and proceed as if you were directly in the system.
Here is a telnet session where you can play some games. This one doesn't require a username or a password.
As the WWW becomes more pervasive, one generally hopes that people will be putting their services on the WWW. It's generally a better way to interact with the public than telnet, but there are some specialized uses for telnet, so you should at least be aware of it. You'll also find more telnet connections in Scott Yanoff's list of Internet services.