Basically, when the pressure is up, the weather is good. Clear skys,mild temps and know wind. The higher barometric pressure prevents lower pressure storm movements from entering the area. Conversley, when the pressure is low, storm cells can and do move into these areas. High pressure moves to low pressure. Animals and some humans can actually feel these pressure changes and react accordingly. That is why I think birds tend to be more active on the leading edge of storm fronts.
-Mathue