Exactly what it sounds like. You know how computer data boils down to a combination of 1s and 0s right? This is just having a program do nothing except write zeros to every sector of the hard drive. One pass of that and all the data is gone, you're basically erasing it at its most basic level.
Pretty much. There's a program called Killdisk which you can write to a floppy and use to zero a drive. Writes every bit to 0. If you're paranoid, you can run multiple passes, but real life isn't CSI...