Answer: The "Gunslinger Law" often refers to the law of "open carry." This means that you can walk around with your pistol in hand, showing everyone you mean business. The name comes from the way it was once used. A gunslinger often faced off against an aggressor in a time when everyone carried a gun. If you were known to carry a gun and somebody shot at you, you were darn well within your rights to shoot him back. "Open carry" came along when guns became unacceptable to just wear around in civilized society but folks still wanted to protect themselves.
Because you are showing everyone how manly you are, this law also means that you can shoot anyone provided you can prove he or she was going to do equal or worse harm to you. You openly displayed your gun, and the other guy had knowledge that you could shoot him if he tried something.
Another law simular to this is the "Castle Law," not to be confused with the "Firefly Law" that also stars Nathan Fillion.
Built off "a man's home is his castle," anyone in your house who you do not want in your house is able to become a piece of modern art by way of shotgun. Texas is an extreme example of this. You can have a gun anywhere in your house and if someone comes in, boom. No questions. Less formal states claim that you have to show that the person meant you harm and was on your property without your permission, so no shooting the maid because she wanted to vacuum at 3am.
Other states, like Mississippi, extend the "Castle Law" to vehicles as well. So if someone threatens you in your car, or more likely your pickup, you can pull a gun from under the seat and see how many holes a human body really needs. If you get stopped and the gun in your car is legal, the police can take it for a while just to see how legal it is, but with the right papers you can have Ole Bessie back and ready to take out car-jackers before it is time to go clubbing. Oh, and they can take you, too, if you do not tell them about it. This is why gun racks are popular. They are a simple way to say, "That's just what I decided to show you."