The mouthpiece connects your buzzing lips to the leadpipe of the trumpet. To maximize our chances to play very well, we strive to find a mouthpiece that feels comfortable, a mouthpiece that easily allows us to move around the horn (attack, range, sound, all around comfort or specialty).
Max Schlossberg recommends buzzing on the mouthpiece for about two minutes before blowing the horn itself. Why? -We recognize that the source of our sound is first and foremost mental. Yet, to achieve that sound that we hear or want, the lips have to produce it. now we are talking about flesh on metal or the other way around. Schlossberg understands that challenge and calls for a taming phase ( that's what I call it), when we need to introduce our bodies to the metal instrument. It is good to also remind ourselves of all the correct things to do on the horn: optimal amount of pressure everywhere (lips, body, hands on the instrument etc...), a very easy breathing mechanism, tongue placement, and overall posture. I am sure there are other personal preferences I am leaving out, but you understand my point.
The mental and physical preparatory setup can take place right then on the mouthpiece, so that, when you blow your first long tone in the instrument, it's not a forced uncontrolled one, which sometimes affect the rest of our practice or rehearsal or delays that sense of ease for some of us. Light unforced tongued and slurred notes on the mouthpiece is all it take have a great start to your daily trumpet practice.