"Fainting goats are a slightly smaller version of the standard goat, who, believe it or not, thanks to a genetic condition called myotonia congenita, actually seem to faint when they are startled.
The names refer specifically to myotonia congenita, a condition in which the muscle cells experience prolonged contraction when the goat is startled. The transitory stiffness associated with these contractions can cause the goat to stop moving, stiffen, and even fall down. This is not a true faint, but a muscular phenomenon unrelated to the nervous system. The actual degree of stiffness may vary widely from goat to goat and is based on a number of factors, including age, species purity, and degree of fright."
Read more about fainting goats here.