High pressure situations are generally associated with fair, sunny weather. As high pressure is an area of sinking air, and air tends to dry out as it sinks, leaving sunny skies.
Low pressure areas are generally cloudy/rainy areas -- where strong areas of low pressure bring our stormiest weather. That's because it's an area of rising air, and as air rises, it condenses into clouds and rain. Air moves from higher pressure to lower pressure, so if you have a high and a low nearby, it can be windy as air rushes between the two.