DirectX is a set of graphics and sound application programming interfaces that let developers address video and sound devices in a PC in a standard way. Ironically, Microsoft originally put DirectX into Windows to entice game developers to port their programs to Microsoft's OS.
But with Vista, Microsoft's own developers have relied on DirectX--and more particularly its 3-D graphics capability--for the fancy Aero interface. It's DirectX that gives Vista that blurred, semi-transparent border around windows. (It's also DirectX that's one of the reasons many existing PCs won't run Vista: Vista requires DirectX 9, and most PCs need an upgrade. Fortunately, it's not a showstopper--you can download it from here.)
Microsoft thinks the Aero desktop is so important that it won't let it be turned off--at least that's what it's telling developers. (I certainly can't find a setting in Vista that will let me downgrade the interface to something less resource-intensive, like the "Windows Classic" look with plain gray borders, even though I might want to.)
As far as I'm concerned, I care about DirectX perhaps even less than I care about games, but I'll bet there's going to be screaming from the gaming community over this--and that's one more community heard from as Microsoft marches toward alienating as many customers as possible with Vista.