The cup is the rounded portion on the inside of the trumpet mouthpiece. Cup sizes are described through a vague system of very deep to shallow. The deeper the mouthpiece, the further the cup slants inward and usually, deep cup sizes are very large. A shallow cup will be smaller and closer to the lip area. A shallow cup has more resistance than a deep cup. Resistance means that the trumpet player must use a faster, quicker airflow to produce a sound. A deep cup requires more airflow, but the trade-off is that there is less resistance.
The diameter of the trumpet mouthpiece refers to the distance from one edge of the rim, directly across the mouthpiece to the other edge. Diameter helps tailor a mouthpiece toward people that have a weaker embouchure. The embouchure consists of the muscles of the lips and mouth and how they are tensed when playing. A larger diameter will make it more difficult to play the mouthpiece, but it will also provide a better, richer sound for those with the necessary strength. Diameters typically range from 15 to 17 mm.
The rim shape provides relief for long periods of playing, but a thicker rim will reduce the ability to play extremely high notes and stay flexible. Thinner rims are designed for players that have extreme control over their mouthpiece. If you use a thin-rimmed mouthpiece, you must avoid the temptation to press the trumpet into your face. If you don't have the strength to play on a thin rimmed mouthpiece using only your embouchure, consider using a thicker rim.
When selecting a mouthpiece, try several different models and thicknesses. If you have thicker lips, you consider a mouthpiece that has a wider diameter and thicker rim. This will help to stabilize the vibrations in your lips. For those with weak or delicate lips, opt for a mouthpiece that is somewhere in between on all specifications. A medium sized rim, a medium sized cup and a diameter of approximately 15 mm.