Booooooooong! Chiming in.
Okay, I'll try to be as short-winded as possible, but we know how
that usually works out.
All spirits categories have rules or guidelines, and the most usual of these is the alcoholic strength, expressed as either alcohol by volume (abv) or proof. There is usually a minimum or maximum abv/proof at distillation, and at bottling. Proof is essentially double the abv, so 45 abv is 90 proof.
Matilda's story is correct. Proof was determined originally by mixing alcohol and gunpowder. Now it's done by lab analysis.
In Rum, there is a category designated as Overproof. Most rum is 80 proof at bottling, and it's cut with distilled water to achieve that strength. Overproof Rum is technically 120 proof or higher. I do not reccomend anyone drinking Overproof neat, as the only thing commending it is the alcoholic strength, so it's suited only for mixing drinks or for young men to prove how utterly stupid and clueless they are in some stupid macho way.
Carrie's story about the Austrian drinking: that would be a curious brand called Stroh (very hard to find in the US, commonly available in Europe). Stroh is rum, made in the Caribbean then shipped to Austria for bottling. The basic one is Stroh 80. The label is a distinctive dark orange. Trouble is, most people who don't know the stuff think "Stroh 80" means it is 80 proof (40 abv). It isn't. Most Europeans use the abv designation...so Stroh 80 is actually 160 proof!
That means when someone pours a shooter (I'm not making this up, guys; they actually do this in Austria, usually around the ski resorts, and they think it's "fun") for the unsuspecting, you get something that is shockingly higher in proof/volume than you should. Usually people wheeze, choke, gasp, turn colors, and do other fun things. I know, as I did it once, a long, long time ago; it was several minutes before I could breathe properly, and my palate was scalded by the alcohol. Some fun, huh?
In addition to the Stroh 80, there is Stroh 40 and Stroh 60. There's also a Stroh Punch, evidently pre-mixed, but I've never had that. Obviously, outside of infantile people who would purposely drink such abominable stuff straight, Stroh 80 is usually used in a Punch mix.
The only use for an Overproof, to my mind, is if you want to flame a cocktail (float a small shot of Overproof on top of the cocktail and light it up. Usually, you let the flame die out before drinking it. Although, in my misspent youth we would have drinks like the Screamin' Yellow Meemie, wherein the doughty idiot drinker, usually already drunk or they wouldn't do it, would down the drink while it was still flaming. You have to do it right, or you will horribly burn your face. I know; a friend did it. Fortunately for him his inebriated state meant he already was anesthetized when we took him to the emergency room for treatment.