High-pressure system
Air pressure anticyclone area of high pressure
A high-pressure system has higher air pressure than its surroundings. It often brings settled weather, but not necessarily sunshine.
A high is a comparison
An H on the chart marks relatively high pressure. There is no fixed minimum value: the surrounding pressure matters. Values are adjusted to sea level so that mountains do not simply appear as low-pressure areas.
What the air is doing
Air sinks over broad areas in many highs. As it encounters greater pressure, it warms. Relative humidity decreases and clouds may dissolve. In the northern hemisphere, circulation around a high is mainly clockwise; in the southern hemisphere it is reversed.
You ordered sunshine and got low cloud
In autumn and winter, cold, moist air can remain near the ground beneath a warmer layer. This inversion restricts mixing. The sky may stay grey while the barometer points to “fair”. Apparently the clouds have not read the label.
Position matters too
Whether a high brings warm or cold air depends on its position and the season. A persistent high can favour a long dry spell. Light winds near its centre do not mean that the edges are calm too.