A high pressure center is where the pressure has been measured to be the highest relative to its surroundings. That means, moving any direction away from the High will result in a decrease in pressure. High pressure centers often represent the centers of anticyclones.
A high pressure center is represented on a weather map by a blue H. Winds flow clockwise around the high in the northern hemisphere. The opposite is true in the southern hemisphere, where winds flow in a counterclockwise around an area of high pressure.
Sinking air in the vicinity of a high pressure center tends to suppress the upward motions required for the clouds and precipitation to develop, which is why fair weather is commonly associated with an area of high pressure.