Air always moves from high pressure to low pressure (like air escaping from a balloon). The different arrangements of these areas of pressure are shown on weather maps. Low pressure is associated with stormy weather, whereas high pressure is associated with clear skies. There are also "fronts" which are boundaries between two air masses of different densities (think cold air and warm air). Often these are associated with a rapid change in temperature. For example, a cold front has warm air before the front, and cold air after the front passes. The front itself usually has stormy weather.

Hurricanes are low pressure systems and move in two ways: in a spiral and across the ocean.

The arrows show the motion of the wind and storm. Illustration by Jiae Hwang.

Coriolis Effect

Because the Earth is round and spinning, objects attempting to move in a straight line across Earth's surface will appear to veer off course. This apparent deflection is known as the Coriolis effect. In a hurricane the central low pressure pulls in air from all directions. However, the air is deflected around the center due to the Corlios effect, causing a swirling motion.

The Earth rotates counter-clockwise when looking down at it from the North Pole
(black arrows). That means that when an object (blue dot) moves from the
North Pole towards the Equator, the object is deflected to the right (green arrow)
of the expected path (red arrow). This is why hurricanes spin counter-clockwise in
the Northern Hemisphere. Earth map courtesy of NOAA.

For more information, please visit:

HRD – FAQ: Why do hurricane winds rotate counter - clockwise in the Northern Hemisphere?

How Stuff Works – Hurricane motion

BBC - Coriolis Effect and Winds

A Wanderlust Short Film on Coriolis