When you put a mouthpiece into your trumpet, there is a space between the end of the mouthpiece and the lead pipe inside of the mouthpiece receiver. This space is know as the “gap” or by the more fancy name “annulus”. You can see the space below:
The theory is that if you can find the right amount of gap, the instrument will perform optimally: Notes will slot better, the scale will be more in tune, and the horn will be more resonant.
Since every trumpet, mouthpiece, and player is different, there is no gap that will work best for everyone. The only way to find that sweet spot is by trial and error, adjusting the gap and seeing what works for you.
A simple way to test different gap settings is to wrap a strip of paper around the shank of the mouthpiece and insert it into the receiver. By adding more paper or taking paper away, you can adjust the gap. If you have too much gap, you’ll have to have metal removed from the shank. Once you do find the optimal gap, you can make the change permanent by having the mouthpiece altered.