Recoil, also referred to as kick or kickback, is the result of Newtonian physics applying itself to your firearm. When the bullet is fired, it is pushed out of the gun at high speed. However, for every action, there is an equal yet opposite reaction. When the bullet is pushed out, it pushes back on the gun, which transmits that force to the shooter. That's recoil.
There are a number of factors that determine how much recoil you'll experience when firing a given weapon.
The most obvious is the power and size of the projectile. A small, low powered round like the .22 Long Rifle, has nearly no recoil in even small, lightweight rifles meant for teaching youngsters to shoot. The .50 BMG, on the other hand, kicks like a mule no matter what weapon you fire it from.
The weapon's weight also plays a role. Long story short, the heavier the weapon, the more easily it can soak up recoil. To experience this yourself, take two weapons that shoot the same round, one heavy and one light, and feel how much more force you experience from the lighter weapon. The .45 Long Colt, for instance, is a big round with a decent amount of recoil. Firing it out of a revolver can be a daunting experience for the uninitiated, but the same round when fired from a Winchester lever action hardly kicks at all.
The design of the weapon also impacts how much recoil you feel. There are a number of different tricks to make a firearm more manageable. Many revolvers designed to fire the S&W .500, currently the most powerful production handgun round on the market, feature vented barrels that direct firing gasses upwards from the tip of the muzzle. This pushes the muzzle down, and greatly reduces the chances of you popping yourself in the face. In my experience, though the S&W .500 is not fun to shoot by any means, it's a great deal less painful than many older .44 Magnum revolvers, despite having a much more powerful round.
Due to a lack of experience, it's not uncommon for authors to over or underestimate the felt recoil generated by a given weapon. For many, especially folks who live outside the United States and don't have access to firearms, their only experience comes from movies and TV shows. Hollywood firearms are specially modified so that they can only fire blanks. Blanks have no projectile, but they simulate firing by burning a load of propellant. Hollywood blanks are specially formulated to produce a muzzle flash, because that adds a visual signature to the act of firing the weapon, something the audience can easily recognize. These blank firing weapons have little to no recoil, which gives people the idea that weapons tend to have no recoil whatsoever. It's one thing to read that recoil exists, and quite another to see your favorite action hero firing a .44 Magnum one handed like it's nothing but a thing.
I tend to err to the other end of the spectrum when designing firearms for submissions. I know full well that firing most production weapons one-handed won't generate enough force to cause injury. A common trick me and my buddies used to use (back before we all got married and couldn't get away with it) was to fire a shotgun one-handed to impress women. Being able to hold a Remington 870 at arm's length and fire it without injury has gotten me more than a few phone numbers. If that's not proof positive that I live in the South, I don't know what is.
When writing submissions, however, I tend to play up the effects of recoil. This is largely because I'd rather writers with little to no experience with firearms treat their character's weapons with respect. It's far too easy to get a little power gamy with firearms, and I'd rather my weapons not get associated with OP douchebags who think they're space Jesus. With the exception of some of my larger anti materiel rifles, you have to act like an idiot to hurt yourself, but if a writer is cautious from the word go, things tend to go a little smoother. Also, it's an easy way to add a tangible weakness to a weapon, which is crucial for making balanced submissions. Balance is essential in RP, after all, and making balanced weapons helps build trust with the Factory.
I would advise any prospective weapons designers to follow suit. Getting a reputation for building weapons that can be abused a kiss of death in an RP environment where reputation is everything. If someone abuses one of your designs, it's always great to be able to point to the original submission and say "No, the weapon isn't overpowered, they're just using it wrong."
Anyway, that's the gist of it. If you have any questions, my inbox and the comments section are open.