What is shell access for?
Shell access refers to logging into the server using your username and password so that you may have direct access and run programs interactively on the server. Usually this is used to run a mail client, manage website files or do network queries. Some people just prefer to have a Linux/unix-like environment. As an example, using the shell, you can run mail clients that respond much quicker (because they don’t have to draw graphics on your screen) and sometimes have better functionality. You can directly edit your website and manage your files. You can also run many other programs that probably are not available on your local computer. Here are a couple screenshots.
