Rising air cools at a rate of 5.5 degrees F for every 1000 feet. When warm moist air rises, it cools. Eventually it cools to the point where it is saturated with water vapor. At this point the water vapor begins to condense out as tiny droplets of liquid water . . . If the air sinks, it warms and the liquid water evaporates causing clouds to dissipate.
Air moves out away from the center of high pressure.
Air must come down from above to replace the air moving away from the high. Thus there is a general sinking or subsidence of air in a high pressure area. High pressure generally brings dry fair weather. Air is pushed toward a low pressure center. The converging air is forced upward.