Everything tends towards homeostasis. Everything tends to uniformity (mountains erode, water cools etc)
Differential heating of the earths surface by the sun warms the atmosphere. The air becomes warmer near the equator than at the poles. This energy gained flows towards the poles. It churns and mixes both horizontally and vertically. It’s messy and has lots of things in the way to affect the flow of energy. Continents, mountains, cold and warm ocean currents.
Warmed air expands and rises. A taller column of air will have a higher weight at the earth’s surface (“pressure”). As you might expect this taller column of air wants to even out towards areas of lower pressure. It happens on a large scale (look up Hadley cell and the trade winds) and on small scales ( look up Foehn winds)
Generally speaking higher pressure means warmer air. Lower pressure is associated with cooling air where water vapor precipitates out as cloud, rain, snow etc.
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