Everything behaves differently under pressure, especially chemical reactions (like making coffee).
With high pressure, the force of the solvent is so high that it’s going to extract solutes faster, and is likely to snag solutes that wouldn’t otherwise be dislodged. Placing gas under pressure makes it more soluble in liquid, which results in more gas content in pressurised liquid. Releasing the pressure will reverse the process, and release gas from solution. A perfect example is opening a bottle of coca cola.
The most familiar coffee brew method that uses pressure is espresso. Espresso machines create a pressure approximately nine times the pressure at sea level. Lots of solutes emerge because of the pressure, and the water will pick a big amount of gas, which causes what we call crema.