Shell servers are unix based systems that provide access to the user and user is given storage space and ability to execute commands and work on unix shell, so if you want to try out operating system like unix you can use shell servers. Also they provide a user with a text based browser like lynx to surf the internet with complete anonymity, but they generally will not let you telnet from them to another server for free (those accounts are paid).
Also if someone is working on windows and cannot install linux then he/she can work on these servers.
They also provide user a home directory but never try to get access to root files it wont be allowed or never try to use shell scripts that can get you root privilidges that wont work either.
Using them requires knowledge of linux commands.

List Of shell servers:

So if you want to see how unix works without the hassles of installing it go and create an account on one of these.