Dungeons and Dragons has had the concept of a "saving throw" for a long time. What exactly is it supposed to represent in the real world? And why is it called a "saving throw"?
The concept of saving throws have been in the game since the original edition of Dungeons & Dragons, and inherited them from wargaming via Chainmail.
The name is a special case of etymological specialisation (where a term becomes so associated with a certain meaning that other meanings are forgotten or diminished in common awareness) combined with some etymological generalisation (where a term loses some of its specificity in order to cover a wider meaning).
Firstly, "throw" originally meant to fling in a spinning fashion, which is an apt description of the accepted way of handling dice so that they're properly random. So, a "dice throw" is just plain English, not a special term unique to roleplaying games. The meaning of "throw" has generalised since to mean simply propelling something, and then respecialised to mean propelling something with the arm. Having lost its "spinning fling" meaning, "throw" now sounds like it must be special game jargon, but it has remained in (less) common usage to refer to rolling dice. Possibly you could consider it a bit of dice jargon that D&D inherited from the long history of dice games.
In the specific case of "saving throw", it was originally just descriptive prose for what to do and why. It's important to know that early D&D was mostly not written with very many defined game terms, rather being described with inexact and ambiguous prose descriptions that more-or-less conveyed the intended procedures of play. Each later edition of D&D was more rigorously written than the last in valiant attempts to make the rules clear of ambiguous interpretations, and many bits of plain language became more codified. Since there is a table in Original D&D that was labeled with "Saving Throw" in capitals, it stuck. Eventually (and when exactly is difficult to pinpoint), phrases like "saving throw" graduated from being plain-speaking English to being technical gaming terms. Why the word "throw" was chosen by Gygax when he wrote that section of the rules instead of a synonym like "roll" or "cast", nobody knows.
So "saving throw" is just some English that was promoted, by accidents of history, to become a technical term in D&D rules.
The meaning of saving throws depends on the edition. In all editions but 4th edition, it is a "hail mary", last-gasp chance to avoid certain death.
Originally, it was not meant to be realistic so much as it was a convenience for making the game more playable. Dragon fire, being ensorcelled, or drinking poison would all normally overcome a person subjected to them. These sort of instant-kill things are potentially fun to play with, and giving adventurers a chance to escape certain death—or worse—means that they could be incorporated more freely. Later editions of D&D used saving throws to model unlikely events that should be easier for more experienced adventurers, making their connection to avoiding certain death less obvious. In these editions, saving throws represent a combination of dumb luck and a measure of preternatural awareness of danger, but they're still more of a player-side mechanic than an "in world" mechanic.
In 4th edition, saving throws are unrelated in game-mechanical terms to saving throws from other editions, since the role previously filled by "saving throws" is modeled instead by a character's various Defense numbers. Term "saving throw" was repurposed for an unrelated mechanical role, which was determining the duration of effects: where other editions determine the number of rounds an effect lasts when it comes into play and the DM or a timekeeper has to keep track of when they will expire, 4e has them last until the player succeeds on a roll to end the effect. Saving throws in this edition represent spells and effects having variable durations combined with the character taking whatever measures are appropriate to rid themselves of the effect.
D&D has had the term "saving throw" back through at least 1e (though I don't have the exact text handy). Supposedly Gygax himself created the term, though I've also heard it was common in miniatures-based wargaming at the time Chainmail was being created (though this may have been referring to the concept rather than the specific term).
It's called a saving throw because it saves your character from bad stuff (a failed save always meant a dead unit in Chainmail; by 3.5 it had expanded to cover relatively minor unpleasantness). While "throw" is the traditional term for rolling dice, D&D has pretty much always used "roll" for everything other than saves; why Gygax chose "throw" over "roll" is unknown (I would personally suggest that it's because people actually threw dice when they failed saves, since a failed save typically represented dead units/characters).
Rocks: One of the most effective and easiest defenses against escalading attackers was a large, weighty piece of rock or stone dropped from above onto the heads of the besiegers. A rock dropped down a ladder will kill the first climber, and the second and third men on the ladder must roll a die to see if they survive, 1 -3 saving the second and 1 -5 saving the third. When thrown down on top of siege equipment and war machines rocks will do 1 point of damage.
From 2nd edition PHB:
Saving throws are measures of a character's resistance to special types of attacks - poisons, magic, and attacks that affect the whole body or mind of the character.
From 3.5e PHB1, pg136:
Fortitude: These saves measure your ability to stand up to physical punishment or attacks against your vitality and health. ... Fortitude saves can be made against attacks or effects such as poison, disease, paralysis, petrification, energy drain, and disintegrate.
Reflex: These saves test your ability to dodge area attacks. ... Reflex saves can be made against attacks or effects such as pit traps, catching on fire, fireball, lightning bolt, and red dragon breath.
Will: These saves reflect your resistance to mental influence... Will saves can be made against attacks or effects such as charm person, hold person, and most illusion spells.
In 3.5e and previous editions, saving throws are your character's chance to resist or avoid unpleasant stuff that doesn't fit in the AC & HP frameworks. It can represent dodging something, or shrugging off its effects through sheer toughness or willpower.
From 4e PHB1, pg279:
When you're under a persistent effect or condition... you have a chance to escape the effect each round at the end of your turn.
In 4e, saving throws are your ability to shake off unpleasant stuff that's already happened to you. It can represent enduring a poison, putting out your burning shirt, shaking your head to get the dirt out of your eyes, or any number of other things.
The concept of "saves" seems to have originated in the wargaming rules of Tony Bath from the late 1950s. Bath's medieval rules have a system such that after a roll is made by the attacker to determine hits, armored defenders make a separate roll to determine if their armor "saved" them from the hit; e.g. "if he has both armor and a shield, a 4, 5 or 6 will save him." The compound "saving throw" was widely popularized in the wargaming community by Don Featherstone's reprinting of Bath's rules in War Games (1962).
Gary Gygax was familiar with Tony Bath's 1966 edition of ancient and medieval rules (Gygax repeatedly credited them in the late 1960s), which use the term "saving throw" freely. From there we see saving throws integrated into Chainmail, where figures roll saves to avoid effects like dragons breath, poison and petrification. Gygax and Arneson's 1972 collaboration Don't Give up the Ship also has saving throws made after ships are hit by guns.
So basically, the original "saving throw" was intended to model the effect of armor, but over time the term drifted to refer to avoiding any sort of effect. From a system perspective, saving throws are used especially to mitigate otherwise unpreventable sources of damage, including area-of-effect damage. See Playing at the World section 3.2.2 for a ton more about this.
I'll take a stab at it. In the real world, in older D&D, it was designed to represent the manner in which your PC endured situations. Fighters used their armor and shield, but they were typically weak to mind magics. Thieves used their perceptions and quickness to remove themselves from harm. Spellcasters used their wills and minds.
The way we typically described it was that a priest had a holy aura that they could evoke that shielded them from damage, or they got Divine Favor. And yes these examples are the way our descriptions tend to be. Makes it better, IMO. Example: PC cleric must make a save versus fiery dragon breath. They make save, my description might be- "You see the gout of flames washing toward you, and you speak words of faith. Your holy symbol flares, and can feel your prayers answered as the brunt of the fire is kept from your body." Example: PC thief must make same save, they succeed, my description might be: "Your keen ears hear the sharp intake of breath and you act without thought, nimbly rolling away. The heat scorches you, but the stones where you stood glow as hot slag." Example" PC fighter, same save, but FAILS: "You steel yourself for the flames, relying on your armor and shied to protect you, but the heat is too great, and you nearly perish. You emerge alive, but severely burned, with smoke flowing from your singed clothing and your armor hot to the touch." Wizards just use their will.
Now, if it was a fighter type who relied on Dex, so be it. You can still apply the same description as a thief/rogue. If they use protection items, then the items can be described as flaring or glowing, etc, and that turns away the flames.