SDN...?
 

After reading the wiki page and five other articles, I'm still not sure I clearly understand what Software Defined Networking is. My main question: Does SDN fundamentally change computer networking in some way? Or is it just some kind of really complicated network administration system?

No
It's actually supposed to make network administration easier.It's just a different abstraction of network processes. Another way to interact and regulate the hardware that exists on the network.
It can't really give you functionality that doesn't already exist, it can only make that functionality easier to understand and use.