This article describes in basic terms the two most commonly quoted models for extratropical cyclone development (cyclogenesis).
The Norwegian Cyclone Model
Early in the 20th century, Norwegian meteorologists formulated a model for an extratropical cyclone that develops as a disturbance along the boundary (front) between the polar and mid-latitude air masses. The disturbance distorts the front into a wavelike configuration.
Wave forms on front (image source: NOAA)
As the pressure within the disturbance decreases, the disturbance assumes the appearance of a cyclone with its characteristic counter-clockwise flow. Southerly winds take warm air northward ahead of the storm and northerly winds bring cold air south behind it. Besides rotating counter-clockwise, the air also flows inward toward the center of the cyclone.