I recently had a customer call who was a little confused as to the operation which differentiated a double action from a single action, so I thought I'd address the issue here:
1.) A single action is an action which requires the operator to cock the hammer back, or rack the slide and cock the striker prior to initiating the firing process in order to allow the firearm to function and thus fire the chambered cartridge. This can be seen in firearms such as: single action revolver (colt sa revolvers and clones, ruger blackhawks, vaqueros, etc,) as well as pistols such as the venerable Colt 1911 and it's many clones, Glock, and Springfield XD model pistols.
2.) A double action allows the operator to pull the trigger or cock the hammer in order to initiate the firing procedure. i.e. it works both ways. Examples of this are German Walther P38s, Beretta M9/92FS, Ruger P98, Ruger Redhawk/Super Redhawk Revolvers, and Smith & Wesson 686s. Each of these are able to shoot in double action mode. Some are DA/SA (double action / single action) while some are DAO (double action only) which only allows double action mode.
Even though a 1911, for instance, shoots and automatically cocks itself and reloads (i.e. it's an auto-loader) it still requires the hammer to be cocked and a round chambered in order to shoot the pistol. The same can be said for Glocks or Springfield XDs, which require the striker to be reset each time in order to initiate the firing process, which, like the 1911, is recoil operated. You cannot fire until this operation is completed.
A Ruger super redhawk, however, allows the operator to pull the trigger, or cock the hammer in order to shoot the round in the chamber, and also advances the cylinder each time the trigger or hammer is engaged. A Walther P38, too, functions similarly to a 1911 in that it is an auto-loader, however, it can operate by simple pull of the trigger, meaning it does not require the hammer to be cocked in order to fire so long as there is a round chambered.
Sometimes these operations can be a little confusing, but if you sit and think about it, the terms do actually make sense.