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"Mach" isn't an acronym, but is in fact named after the Austrian physicist Ernst Mach, who in 1877 published an important scientific paper laying out the principles of supersonics. He also came up with the Mach number, which is the ratio of the velocity of an object to the velocity of sound. A plane traveling at the speed of sound, therefore, has a Mach number of 1. It's important to note that Mach 1 doesn't simply stand for the speed of sound, but rather the speed of an object traveling at the speed of sound. Ernest Mach was also the first to correctly describe the sound effects produced during the supersonic motion of a
projectile (BOOM!), and he observed the existence of a conical shock wave formed by a projectile as it approaches the speed of sound. It was this conical shock wave that led to a lot of deaths in the quest for supersonic flight. While many test aircraft had the capacity to surpass the speed of sound before Chuck Yeager's breakthrough in 1947, they weren't designed to withstand the "wall of air" that occurs at around Mach 0.8. You can read all the details of Yeager's supersonic flight in his official report.
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