A high pressure is a term used by weather forecasters to tell of a large area of calm air.
Air is always moving about the world. It tends to do this in great spirals. If you saw the same thing in water you would call them eddies.
When air spirals upwards, it tends to bring warm and cold air together, and as the air rises so it cools and releases its moisture. This produces rain. That is a low pressure (or depression, or cyclone).
For every area of upward spiralling air, there must be a place where air spirals downwards. That is called a High Pressure, or anticyclone. When air spirals downwards it tends to spread out and get warmer. So this event stops moisture turning to rain and high pressures are always connected to fine, settled weather.
Just because it is a high pressure does not always mean that the weather is nice, however. In summer, high pressures are often connected to hot, dry sunny spells, but in winter, when the air is cold, it often causes dull weather, something weather-forecasters call 'anticyclonic gloom'. This is dull, damp weather that can last for weeks. It is when we get our coldest weather.
The video below gives an example of mist and fog that develop in winter with a high pressure.