I'm a Shodor System Administration Intern!
>>> What exactly is system administration?
"System administration" is a pretty broad category. In general terms, system administrators create, manage, and maintain an organization's network, services, hardware, etc. Their functions can range from repairing broken hardware to securing a network against outside intrusions to maintaining regular back-ups of data to, well, basically anything that needs to be done.
>>>That's all well and good, but what specific things do you do?
I could write a lot of very general paragraphs to answer this, but I'm not sure how useful that would be. Instead, let me describe some specific projects that I've worked on / contributed to as a system administration intern at Shodor.
>>> What exactly is Shodor, anyway?
I always have trouble explaining exactly what Shodor is, because I find that the words 'comptuational science institute', which are the first that come to mind, don't really conjure my intended image. So why don't you take a look at the Shodor home page and see if that answers your question better?