A hoof was the tip of the toe, located at the end of the foot of certain even-toed mammals, comparable to a toenail. Animals such as horses, cattle, giraffes, camels, pigs, goats, sheep, deer, white rhinoceroses, and buffalo.
They were also present on mythological creatures, such as the Satyr, a species found on Megas-Tu. (TAS: "The Magicks of Megas-Tu") The t'stayan was considered to be "a very powerful beast", native to Talar, that had six hooves. (TNG: "Suddenly Human")
A verse from the song "The Frogs", as sung by Alexander, referenced the Great Pan, who "sounds his horn. Marking time to the rhyme with his hoof, with his hoof." (TOS: "Plato's Stepchildren")