In general, that just means that they give you full root access to your system. Most of the time, they provide this via a remote ssh terminal. By default 99% of server providers will just give you command-line access, but with that, you have the ability to install a graphical environment if you choose. You'll need to use remote X or VNC to display the GUI environment, though, as most providers won't let you get access directly to the console of your server, especially if it's a VPS.
With full root privileges, you can do whatever you want on the server. That is, as long as you stay within the AUP of your provider. This includes installing applications, copying data, adding users, setting firewall rules, and whatever else you want/need to do.
As an aside, though, if you're serious about learning how to administrate a linux server, I'd highly suggest not installing a graphical environment. Yes, there's a steeper learning curve to the command line, but once you learn it, it'll stick with you your whole life and you won't ever regret learning that skill.