Here can you read about some common usage scenarios for a UNIX shell.
Many scenarios are targeted towards IRC, but as you might know you can run IM clients for AIM, Yahoo!, MSN and several other chat networks. You could also use it to run an email client or a text editor for similar reasons.
1. Multiple computers
Issue: You have several computers, one at home and one at work for example. You want to keep your settings in your IRC client as your change between the computers. Also, you don't want to miss pieces of conversation while you change between the different computers.
Solution: You can use an IRC client like irssi and run it in a screen on the shell. This program will always keep on running on the server, even after you log out, and you can connect and resume from any computer at any time. You will have a consistent environment with the same settings etc and you will not miss anything being said while you are away!
You can even resume your IRC session from your smartphone with something like Connectbot for Android. If you're using weechat you can use this neat web interface: Glowing bear.
2. Unstable network
Issue: You have a laptop and you move between several different wireless networks, or your wireless network is not very stable. You don't want to get disconnected from IRC and miss conversation.
Solution: You run IRC from the shell. This way you can read the backlog when you get connection, and you won't get disconnected from IRC.
3. Evil firewall
Issue: Your computer is behind an evil firewall that doesn't allow you to connect to IRC.
Solution: You connect to the shell and use IRC from there to bypass the restrictions. You can even connect to the SSHd on port 443 if your firewall only allows web traffic.
4. Share files
Issue: You want to publish some files and share them with your friends. Some photos of the latest party or whatever.
Solution: You upload the files to your webspace at the shell and anyone can access them. You can also place restrictions on who can access the files, including allowing specific IPs or require a login.
Issue: You want to have your own cool blog, personal website etc, website or maybe a little forum.
Solution: For free accounts you can publish a site or blog via static HTML, give hugo a try for example.
For supporter accounts you also have the option of dynamic pages via server side scripting languages installed on the web server such as PHP or Python and store data in a database like SQLite or MySQL. One of the most popular CMS/blog platforms is Wordpress.
6. Learn UNIX
Issue: You want to learn more about UNIX environments, how to manage files and permissions etc.
Solution: You get an account and play around as much as you like!
Issue: You want to talk to other people interested in computers, maybe specifically UNIX environments and networking.
Solution: You become a member to be a part of the community and talk to other users and make new interesting friends.