The link between mad cow disease and human CJD is only beginning to be understood. Both appear to be caused by an agent that isn't a virus or bacterium or any previously recognized form of life. It seems to be a simple protein called a prion, though proteins are not supposed to be able to reproduce and go around infecting things. One more bit of background. There it is called kuru.
Cannibalism seems to be a key factor.
The mad cow outbreak may have started with the modern practice of cooking up dead sheep and using them as a cheap protein supplement in cattle feed. Sheep suffer from a brain-degenerating disease called TSE or scrapie. The theory is that somehow a scrapie prion jumped the species barrier and infected a cow. When that cow died, it too was sent to a rendering plant and turned into feed, thus spreading the disease. Hence the European beef panic, the incineration of thousands of British cattle, the skittishness of Europeans about their food supply, and a death sentence for about 300 sheep.