SSH stands for Secure Shell and is a secure method of accessing remote systems. Wit SSH, you can login to your Linux or Unix shell command prompt and execute commands as if you were sitting right in front of the server typing at the console.
Before SSH, people used Telnet to access servers. Many university students from the 80s and 90s may even remember having telnet accounts. Unfortunately, telnet is not secure, so as the world became more open to the Internet, servers connected to it needed a more secure method of accessing the shell.
SSH provides encryption for data transfer that prevents would-be attackers from accessing your password and user information. For this reason, another advantage of SSH is that you can use it to tunnel other protocols. For example, if you want to transfer files securely, you can use SSH to encrypt your FTP transfers. You can do this with just about any type of connection, such as VNC or Samba.
With SSH you can manage your dedicated server remotely, monitor logs, install applications, start and stop services, and even manipulate databases. It recognizes normal Unix commands, and you can use it to login as root for full system administration.
SSH is the most secure and reliable way to manage your server. With it you can do far more than you could with a web-based control panel. Therefore, while it is probably not a replacement for a graphical interface, it makes an excellent and necessary supplement.