Take a rifle you can make "safe" like an FAL or an AR. Open the receivers, remove the bolt and cock the hammer.
Close the action and line up on a target. Hold the gun steady. With your trigger hand not on the pistol grip "pull" the trigger until the hammer falls. Note how far off the sights are.
Repeat, but this time have a firm hold on the pistol grip. Hold the rifle steady, on the target, but slowly squeeze the trigger until the hammer falls. Note where the sights are.
The terminology may be what's throwing you, but the point was to try and get the student to realize the fast uncontrolled movements to fire the weapon will result in pulling the firearm off target.
Smooth, controlled actions, however, are more likely to maintain proper sighting.
Same is true in dealing with a lot of machinery. I once explained to a buddy of mine when racing sports cars to think about the throttle like a trigger, that it needed smooth, controlled inputs to keep from upsetting the car. Note that smooth does not necessarily mean slow, nor does fast mean jerky, but it takes skill to be both fast and smooth.