BSE (at least in terms of veterinary medicine) stands for Bovine Spongiform Encephalopathy.
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Bovine = Of, relating to, or resembling a ruminant mammal of the genus Bos, such as an ox, cow, or buffalo.
Spongiform = Resembling a sponge in appearance or texture; spongy
Encephalopathy = Any of various diseases of the brain.
(Source: dictionary.com)
Why is is called "Mad Cow" disease?
BSE is a relatively new disease, first diagnosed in Great Britain in 1986. The common name of "Mad Cow" is probably due to the loss of motor control, dementia and behavioral changes seen in the late stages of this disease.

