Internal Climate Variability                      Some key concepts:
Recall that high pressure is associated with cold temperatures and sinking motion.  The sinking motion occurs because surface air moves away from the high pressure center under the influence of gravity, and draws down air from above. 
Conversely, low pressure is associated with warm temperatures and rising motion.  The rising motion occurs because surface air converges on an area of low pressure under the influence of gravity, forcing rising motion over the low. 
Thus a low often brings precipitation with it, while a high bring clear skies.