As any high schooler who has incisively compared bottles in his or her parents' liquor cabinet can tell you, a spirit's proof is exactly twice as much as its percentage of alcohol by volume. Why bother using this 0-200 scale? Because history, of course.
"Proof," as it's used in regards to booze, harkens back to when traders would have to literally prove that their hooch was the real deal. According to the University of Cincinnati's William B. Jensen, in 16th century England, traders would drench a pellet of gunpowder in liquor to determine the spirit's potency. "If it was still possible to ignite the wet gunpowder, the alcohol content of the liquor was rated above proof and it was taxed at a higher rate, and vice versa if the powder failed to ignite.”
While the term "proof" stuck, in America, the standard it refers to has nothing to do with gunpowder. Around 1848, 50% alcohol by volume was chosen as a baseline and 100 was used as its corresponding proof. Thus, the proof is double the ABV.
In other countries, other proof systems are used. For example, in 1816 the U.K. started to use gravity as their standard. The Customs and Excise Act states that 100 proof liquors are "those in which the weight of the spirits is 12/13 the weight of an equal volume of distilled water at 51° F (11° C)." The proof then comes out to be about 1.75 times the alcohol by volume percentage. All that math could drive someone to drink.