A 1-frame (or “0-frame” or “instant”) throw, is a throw for which the throw hitbox appears just after the command input registers (hence the number of “frames” mentioned).
This usually refers to a command throw, but depending on the game’s system, it can apply to a normal throw as well.
There are very few moves indeed that start up in one frame that aren’t throws, so it is extremely important to know whether or not a throw falls under this category.
1-frame throws can be used for their speed in many situations, such as an empty throw, or when you know where the opponent will be on the ground, such as during their wakeup attacks or while you are pressing a mixup. This puts serious pressure on an opponent’s blocking strategy, so depending on the character, whether or not someone has a 1-frame throw changes up abilities a lot.
Also, it is not entirely false that throwing after blocking a jump attack makes these a sort of pseudo-anti-air, but when the opponent also has a character with a throw, trying this too often will make you highly susceptible to empty throws yourself.
Examples include Zangief’s Screw Piledriver, Clark and Ralf’s Super Argentine Backbreaker, and Daimon Gorō’s Tenchi Gaeshi.
In The King of Fighters ’97, command throws do not have a missing animation, so nearly all throws are, in practice, 1-frame throws.