Fedora, CentOS and Ubuntu are all Linux OS Systems, meaning that they are also all open-sourced, community supported operating systems.
Fedora - enterprise level, constantly updating, not as user friendly, more for advanced Linux admins. The constant updates also tend to affect the stability of the OS.
CentOS is a highly stable enterprise-level OS known for reliability. Updates not common, security updates included are stable & prevent applications from compromising any of the security of the system, best choice for hosting servers.
Ubuntu is the most user friendly of the three, and the most popular, with a regular update schedule and the largest support community. Ubuntu is catered more for personal use, and currently has the largest reach of the three, with platforms on mobile devices and tv's, and a new desktop project focused on chinese users.
Advantages: data transfer encryption, you can use it to tunnel protocols, manage your dedicated server remotely, monitor logs, install applications, start/stop services, manipulate DB's, login as root, manage your server.
Administrative Tasks to be done with Shell: Create a public/private key pair for authenticating yourself and encrypting your communications, log in with Secure Shell, Port forwarding in Secure Shell, copy files with Secure Shell, connect from a host inside a firewall to a host on the outside, transfer files with Secure Shell.