What is S-OFF? Why would I want to do it? I always root my android devices, but there's something called obtaining S-OFF for certain devices, and I have no idea what that means.  What exactly does the term S-OFF relate to?  Why would I want to obtain S-OFF for my device?
If you have a locked bootloader, it's S-ON.  If you fully unlock the bootloader it's S-OFF.  As eldarerathis notes below there's an intermediate state, where it's unlocked but still S-ON, where you can flash recoveries and ROMs but not radio firmware and so on.

If you don't unlock the bootloader, you can't flash unsigned firmware and most often can't alter your ROM (i.e., no permanent rooting).  The locked bootloader generally restores a known good system image on boot if it sees that changes have been made.

For some devices there's no known method of unlocking the bootloader; most of the time you need something official like HTC's unlocker tool.