Air Pressure in our atmosphere is measured by Barometers, instruments designed to react to the downward force off all the air above us. Much like a bathroom scale that we get on to weigh ourselves, barometers "weigh" the atmosphere.
If the air above us is sinking, or pushing down toward the Earth's surface, it weighs more. With a bathroom scale, if you weigh more, the numbers go higher. Well, when the air is sinking, and weighs more, the reading on the barometer goes higher. Since it is going higher, we call sinking air High Pressure . And, because clouds generally form when air is rising, when it is sinking, clouds do not form...in most cases. So, high pressure brings clear nights and sunny days.