Flash has had hardware acceleration "forever", or at least as long as I can remember. I suppose it did not back when it was always called Shockwave Flash, but in those days there probably was not much hardware acceleration to take advantage of.
The purpose of hardware acceleration is to allow Flash to do its job while using less CPU, instead letting the GPU hardware do some of the work. On a computer with a slower CPU, this may be the difference between getting smooth video or something closer to a choppy sequence of poor quality still photos. For more modern computers, this should allow the machine to produce smooth, high quality video while allowing the CPU to work on other things.
Flash 10.1 upped the ante by adding hardware decoding, which means the work of decompressing highly compressed video formats like H.264 could be performed by GPUs with this capability built in. The 10.2 iteration of Flash introduced Stage Video, which "helps websites deliver best-in-class video across screens and browsers by enabling access to hardware acceleration of the entire video pipeline."
After upgrading to Flash 10.2, I was left asking "why is Flash still hogging my CPU?" Watching March Madness On Demand from my old-but-serviceable everyday desktop (Athlon 64 X2 3800+, Windows XP SP3, GeForce 8400GS graphics), for example, pinned the CPU between 90 and 100%. Other video sites like ABC and Hulu ran at about 50% CPU, effectively monopolizing one of the two CPU cores.
I wondered whether I needed to upgrade to a newer, but still entry level, video card like a 220, 240, 430 or 440, or whether the DirectX 9 limitation of Windows XP was a problem. However, when I checked out Stage Video on Adobe's site, I ran the examples and found that 720p video scaled to full screen could run at under 15% CPU. The Big Buck Bunny demo is especially cool, as it allows you to turn Stage Video on and off to compare CPU usage.
After a little thought, my suspicion is that sites like ABC and Hulu use Flash plug-ins or other code that prevents the Stage Video pipeline from working, probably to implement digital rights management (DRM). Maybe the problems are related to the way in which the videos are encoded or streamed. In any case, other sites for which this seems to be true include Crackle, The WB, PBS and CBS.