Embouchure
The setting of the lips on the mouthpiece.
What it means
Embouchure (German mostly Ansatz) designates the whole setting of lips, corners of the mouth, jaw, and facial muscles when playing a wind instrument. With brass players it is especially consequential, for there the lips themselves vibrate and form the actual organ of tone production: the airstream sets them in vibration, and this vibration excites the air column in the instrument. How tense the lips are and how large the opening between them is determines which note of the harmonic series responds.
Musical use
Because brass instruments only switch between different harmonic series by valves or slide, the embouchure decides the pitch within a series. The higher the note, the faster the lip vibration must be. From this follows much that matters for instrumentation: high registers are strenuous and cannot be sustained for arbitrarily long, and a player needs rests to recover the embouchure. Tone colour, response, and intonation also depend directly on it; a well-supported embouchure sounds even, a tired one becomes uncertain and flat.
Performance practice
The embouchure is not pressed but held: the corners of the mouth stay firm, the centre of the lips stays flexible, and the pressure of the mouthpiece on the lip stays as slight as possible. Too much pressure is the most common cause of quickly failing endurance. Practise slurs across the partials and long, quiet notes daily, because both train fine control; loud high notes alone train mainly strength. In long pieces, plan deliberate phases of recovery and take the instrument from the mouth in them. Take care that the air stream does the work: where the breath carries, the lip has to do less.
Remember that the embouchure develops over years and changes are to be made with care: a change of mouthpiece or of the placement affects everything and should be put into calm times. Practise daily in short units rather than rarely and long. After breaks of several days, check whether endurance and response have slackened, and build them up again step by step.