It is technically nothing new, Nvidia teamed up with Havok years ago, but the 'how' side of the question means AMD just won the argument.
The big thing that AMD did was code the Havok implementation in OpenCL. This means that it is a standard, and any other OpenCL supporting GPU, Nvidia, S3 or Intel can use it on their GPUs as well. As long as you have OpenCL drivers, you will have Havok GPU-accelerated physics.
There were two Havok demos, the standard train bridge demo and a woman in a red dress for cloth simulation, and one AMD demo. The AMD version is tentatively called the samurai demo, and features a martial artist in a stone square doing some acrobatics with a spear. Ribbons on the spear flow realistically, and flags blow in the breeze.
If this doesn't sound all that spectacular, it really isn't. The Havok demos are pretty standard, and the ATI one doesn't break new ground. The part that is spectacular is that it was all done in a handful of weeks. A quarter ago, this didn't exist, and now you have a full Havok implementation on the GPU, written in a standards-compliant way. It wasn't all that fast, yet, but it did work seamlessly.
Don't underestimate how big a deal this is, however. As soon as it is optimised correctly, you can parse the physics load between the CPU and GPU. If you have more of one than the other, you can still use physics in the way it was meant to be played. Oops, wrong slogan... but this implementation should actually do what the other side promises. The upshot is that game developers can use physics more liberally, they don't have to worry about minimum specs as much.
Correct use of resources, not bluster, ulterior motives and branding, will bring physics to the PC gaming market.
Given what was accomplished in a few weeks, expect to see this for real in a quarter or two, then the game changes for real.