Watch a person hammering a nail. Most of the arm movement is from the elbow, forearm, and wrist. This is what keeps the hammer accurate. If you try hammering with the whole arm, you will notice a sudden decrease in accuracy. This motion from the elbow and lower arm is where the hammer principle is derived. When applying this principle, the arm movement of a punch is basically the same as the hammering movement, from the elbow, forearm, and wrist.
Using the hammer principle helps prevent telegraphing of a punch. Experienced martial artists and boxers usually keep their lead arm moving constantly to conceal the initiation of a punch. If the arm is already moving, there is no initial movement for the opponent to detect. This is where the hammer principle comes into play. While you are making these small motions, keep your lead elbow in the same spot so nothing is moving except for the forearm, wrist, and hand. Keeping the elbow immobile is also discussed in the immovable elbow paragraph covered in the blocks topic.
To execute a jab, from the immovable elbow, drop the lead arm to a level where the forearm is pointing straight at the opponent’s nose and fire the punch. If done properly, this motion will conceal your intention to strike. This is what is referred to as “dropping the hammer.” Think of your forearm as the barrel of a gun. The fist is the bullet. Wherever you aim the barrel, the bullet goes. If the barrel is always pre-aimed, it is always ready to fire, so, as the lead arm is constantly moving around, always “track” the opponent’s nose with it. Then you may drop the hammer at any time.