Linux is an operating system like MS Windows, which allow software programs ("application software") to interact with the computer. An operating system makes the computer hardware (say, a microprocessor) understand the commands of application software and gets the job done.
Server/system administration of Linux is all about keeping a Linux-based computer in usable order. Administration involves functions like backing up files, installing new programs, creating or deleting user accounts, making certain that the filesystem is not corrupted, and so on. In short, if a computer were a house, system administration would be can be likened to maintenance - things like cleaning, fixing broken windows, etc.