Most people read "system" to mean an individual computer, and think that all a sysadmin does is clean viruses off your computer and replace your monitor.
A real computing system is larger. Very few computers work just on their own anymore. When you use the web, play a game online, share files with a friend, or send email, you're using a complex and intricate collection of computers, networks and software that come together to do the job you're asking.
A sysadmin manages these systems. They figure out how to bring storage from one server, processing from another, backups from a third and networking from a fourth computer all together, working seamlessly. For you.
It's not an easy task. Your sysadmins need to understand in depth computing protocols. They often have to know something about programming, something about hardware, a lot about software and even more about the people using their system.
A sysadmin is a professional, with complex skills and a daunting job. Many people find computers difficult to use and sometimes they're unreliable. Being a sysadmin doesn't absolve someone of dealing with unreliable computers. No one sees more dead computers in a day than a sysadmin. No one sees them doing truly baffling things, and no one has more stories of computers failing, acting possessed, or even catching on fire.
Their job is not only to be the geek in the corner who types all day. What they're doing is bringing these diverse pieces of technology into order, and fitting them together to fill your needs.
Being a sysadmin takes a certain boldness, to be one of the first people to take on the challenge of turning difficult computers into easy to use systems. But hundreds of thousands of people are working in that field now, from the entry level help desk tech to the corporate CIOs and everyone in between.
So when you think of a sysadmin, think of the people who run the servers, the people who make sure your data is safe, the people who manage your network, the people who monitor it for security and the person who cleans the virus off your computer!