Normal hard drives, like the one in your computer (unless you've already shelled out a ton of cash for an SSD) have discs in them that spin, and they take time to find the information stored on them -- that's why, when you double click your WoW icon, it takes a few seconds (up to a few minutes if you've got a slower computer) for your WoW window to load up. But a "solid state" hard drive doesn't have discs or moving parts -- it's essentially one big block of memory -- so it's much, much faster in terms of retriving information. And what's going on in the video on their website is that they're pulling so much information from the hard drive that WoW is installed on that it's taking only seconds to load up thirteen windows' worth of WoW.
Of course, how fast all of those windows actually run depends on a lot of other things in the computer -- you'd need a lot more than just an SSD to have the video power to run 13 separate 3D windows at the same time (though TGDaily says they weren't breaking the bank at 5 instances running, they just didn't have any more accounts), not to mention the bandwidth that would come from 13 different connections. But just the startup is interesting enough -- eventually these SSD drives will become cheap enough to be used all over the place, and information will be almost instantly accessible from wherever it's stored on your PC.