Single-action and double-action refer to how a gun's mechanism operates when the trigger is pulled.
A single action revolver has a light and smooth trigger pull, as it only needs to drop the hammer.
This allows for more accurate shooting.
A double action revolver has a heavier, longer trigger pull, which can be detrimental to accuracy.
In a single-action, when the trigger is pulled, the hammer is released, causing the cartridge in the chamber to fire.
They are called “single action” because only one mechanism – the release of the hammer – occurs when the trigger is pulled in order for the gun to fire.
Single action automatics such as the 1911 patter pistols must be cocked manually prior to the first shot, but on subsequent shots, the hammer is cocked automatically by the reward travel of the recoiling slide.
Some consider double action weapons to be safer than single action weapons, but modern innovations have made it very difficult to make a well maintained firearm of either type unintentionally discharge.
The hammer cannot be manually cocked back in double action, only the pull of the trigger can cause that to happen.
A double action revolver can be reloaded more quickly, by swinging the cylinder out of the gun frame, and then using a speed loader or hand-loading the rounds.