A high pressure system refers to a weather event. Here is the definition.
As to fish biting or not during one, I don't know.
HIGH PRESSURE SYSTEM
An area of relative pressure maximum that has diverging winds and a rotation opposite to the earth's rotation. This is clockwise the in Northern Hemisphere and counterclockwise in the Southern Hemisphere. It is the opposite of an area of low pressure or a cyclone.
From http://www.weather.com/glossary/h.html
Generally, a high means good weather and a low means bad.
If you have arrived here by accident, I suggest panic!