Well DDR itself is rather simple
It's still SDRAM, on a 100 or 133Mhz clock cycle. A clock cycle is a square wave and data transfers in regular SDRAM are keyed to one edge of the square (there is a falling edge and a rising edge, I believe SDRAM uses the falling but it doesn't really matter, it's one or the other but not both).
DDR SDRAM is still SDRAM on a square wave clock cycle, the only difference is that it's data transfers are keyed to both edges of the clock cycle, therefore you get 2 data transfers per cycle (hence Double Data Rate).
So you get an SDRAM equivilant clock speed of 200 or 266Mhz, so you get twice the bandwidth.
(The numbers 100 (200) and 133 (266) are for main system memory, the numbers involved in Video cards are much higher, but the concept is the same)
But "what" it is isn't really important, how does it affect performance, and how does it affect price are
The performance impact on Video subsystems is rather profound, the impact on Main system memory isn't all that much. Look in Anand's archives for AMD760 or ALi MagiK1 reviews, they both use DDR and will be compared to chipsets that don't use DDR. The new Gigabyte board a few points down the front page is DDR for the P3, also compared to SDR chipsets.
For DDR on video cards the article biggs gave is a good choice, GeForce256 SDR vs DDR and also Radeon 32MB SDR vs 32MB DDR are the only fair comparisions you'll find, the Radeon and GF256 were the only chipsets with both SDR and DDR boards built on them.