Mad cow disease, and its human equivalent, new-variant CJD, are what are known as prion diseases. Prions, believed to be the smallest infectious particle, are tiny hydrophobic proteins.
Diseased prions alter the shape of normally-occurring prions in the brain, resulting in the disease.
When the bovine variety erupted in the U.K., there were fears that an epidemic might sweep that country, potentially affecting anyone who ate beef. That epidemic never materialized but a new study says the risk of an epidemic is still real, it might just be delayed. Studies on mice show some individuals quickly develop the disease because they're more susceptible, but the other mice aren't immune, they just have a longer incubation period. If the mouse model holds true for humans, it would mean that only a small fraction of people with the disease have already become sick. The rest would still be incubating it, perhaps for decades.