Admins (short for Administrators) are essentially gods. They are responsible for maintaining and upgrading the server - basically everything behind the scenes. Currently they are the only people who can whitelist players (although under normal circustances Mods should be able to do this as well).
There is no fixed process for how people become elevated to the level of Admin. It is determined by who can fulfill the needs of the server, and possibly by sacrificing a small goat.