[CME]

Yep it's pretty simple really. You want to discharge any electricity before working inside the computer. You do this by touching something grounded. In this case it's the PC case which is grounded through the power supply which is grounded through the round longer pin of the electric cord (assuming a US power cord) going into the wall socket.

If the switch on the power supply is off, and by all means it should always be off when doing something inside the case, no power will pass. I promise. So by leaving the computer plugged in, the case still has a path to ground should you move around and build up more static.

If its not connected you could possibly (but very unlikely) short something out if you move around and build up electricity and the touch something inside the case. Whether or not you touched the case beforehand as there is no path to ground.

The odds of you building up enough static charge to damage anything is so slim it's not funny but that's why you should leave the cable plugged in. Just in case you do manage to be really staticy.