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"Racking" refers to pulling the slide back and letting it go. It has a spring that is compressed when you pull it back, and when you let go the spring will drive it forward. When it moves forward it will pick up a round of ammunition from the top of the magazine (this is called "stripping" a round from the magazine) and put it in the chamber, ready to fire.
At this point there are actually three kinds of semi-automatic pistol actions: single-action, double-action, and double-action-only, and more than one way to load them for carry. With the single-action, or double-action, you can load a magazine, but not rack the slide. With either one, you then have to rack the slide to prepare it to fire. When you do, the hammer will be cocked, so either type will then fire. When the gun fires, the recoil energy is used to cycle the slide back and put a new round in the chamber. This cocks the hammer so the gun can be fired again immediately. Double-action will work the same by this method. Where the difference lies is when, after racking the slide, you put your thumb on the hammer and depress the trigger and use your thumb to let the hammer down slowly and without firing. In this condition, the single-action will have to be cocked once with your thumb or by racking the slide again (ejecting and wasting a round of ammunition), where the double action has a longer and heavier trigger pull that cocks the hammer and releases it by pulling the trigger alone. No need to cock the hammer separately in the double-action.
When the first double-action shot is fired, the gun will operate itself and cock the hammer for you for the next shot. This means the trigger is easier to pull on follow-up shots since it isn't also having to cock the hammer again.
If you want to be able to use a single-action quickly, you usually cock the hammer and put the safety on. This is called "cocked and locked". You need to learn to flip the safety off as you bring the gun to bear on a target. The double-action may be carried with the hammer down, and you depend on being able to use that first, harder trigger pull to bring it quickly into action. This is supplemented by use of the safety.
The third type is double-action-only. This is favored by some police departments. In this type, the hammer never stays back in the cocked position. Instead, the shooter must use the harder and longer trigger pull to fire the gun every time. Its action will still cycle and it will still load the next round from the magazine automatically. The harder trigger pull is thought to discourage accidental discharges when a tense situation fills everyone with adrenaline. It also makes trigger operation consistent from round to round, instead of being harder on the first shot and lighter on the rest, as the double-action is. That problem may, however, be circumvented in all guns by following the practice of keeping your trigger finger outside the trigger guard (the steel loop surrounding the trigger) and laying alongside the frame of the gun until you have a definite target to shoot at. I believe this practice originated in the Marine Corps. It was promoted by Jeff Cooper, and now seems to be nearly ubiquitous.
As a point of marksmanship, most people find it more difficult to learn to use a double-action trigger as well as they can a single-action trigger. The single-action has the light trigger all the time. The double-action will, too, if you opt to keep it cocked and locked like a single action. It is only if you set the hammer down that it makes a difference. A double-action or a double-action-only gun will snap the hammer every time you pull the trigger on an empty magazine. This means they may be dry-fired (no ammo; a common way to practice seeing the sights on a target and learn to work the trigger without disturbing the sights) without cocking the hammer each time.
