To understand the forces that drive a hurricane, we must first understand the forces that drive a heat engine. An engine can be abstracted as a heat source, a conversion mechanism and a heat sink. For example, if we consider a steam locomotive, the heat source is the fuel and the firebox, the conversion mechanism is the piston and cylinder, and the heat sink is the environment into which the exhaust steam escapes. Likewise, a power generation plant has a heat source such as a gas or oil burner, converter such as a steam turbine, and a heat sink such as a cooling tower. In fact, the characteristic tower shape associated with the cooling process of a nuclear power plant is the "heat" sink associated with this type of power generation process.
To apply our "engine" abstraction to the process of a hurricane, we must first identify the heat sources and sinks. To do this, we consider the now familiar satellite view of the hurricane. We will notice that at the center of the hurricane, we see the white of the clouds as viewed from space. This implies that at the core of the hurricane, the storm is reflecting the sun's energy back into space. ( and thus the clouds appear white, the color of all the wavelengths in the color spectrum.
But outside the body of the storm, we see the blue of the ocean. This implies that the sun's energy is entering the sea water, it is being absorbed, and consequently heating the ocean, and only a small amount of blue light is being reflected back into space. Thus, the blue water, absorbing the suns energy will be considered as our heat source, much like the firebox on our previously considered steam engine. And just as a firebox causes water in the liquid state to change into water in the gaseous state in an engine's boiler, the heating of the sea water by the sun causes water vapor to leave the ocean and go into the atmosphere. This causes a rather familiar process we all know as cloud formation, and equally familiar is the process of condensation and rain. Thus, we know have identified and hopefully understand the heat source of our engine and the heat sink, or condensation phase of our heat engine.
Lets turn our attention to the actual mechanism of the hurricane's engine. As water vapor cools and causes cloud and rain formation, it causes a drop in pressure. As we know from our high school physics class, pressure is dependent upon temperature. ( remember pv=nrt ? ) As temperature drops, air pressure drops. But as a more sophisticated principle, one we learn in thermodynamics states, as pressure and temperature drop, so does the airs ability to hold water in the vapor form, so in fact the process of condensation is accelerated.
We know that air flows from high pressure to low pressure, so we can easily see why air flows from the perimeter of the storm to the center, but why does it go around in circles, instead of going in a straight line? To answer this question, we must go to a branch of geophysics that deals with geocentric forces known a Coriolis forces. The study of Coriolis forces has to do with how the nature of forces are changed if they are on a scale where we must consider the rotation of the earth. If we consider the earth to be like a merry-go-round, and consider a moving object to be like a ball thrown from one person to another on a merry-go-round, it is easy to see that the motion of the merry-go-round must be taken into consideration in order to compete our pass. Likewise, as our hurricane model, the rotation of the earth causes the hurricane to turn in a counter-clockwise motion, as the molecules in the atmosphere are affected just like a ball that is thrown from a merry-go-round.
At this point we have created a model where water evaporates from the ocean, driven by the Sun's energy, moves into a rotating cloud, and condenses due to the cooling affects that the cloud imparts by reflecting the Sun's energy back into space. But there are a few more forces that act synergisticly that we must consider. The pressure measured in a gas, such as the atmosphere is also a function of the velocity that it is moving. This is known as Bernoulli's principle. It is Bernoulli's principle that allows an airplane to fly by having a more curved surface on the top of the wing than on the bottom. In this example, the longer path the air must travel over the top of a planes wing, increases it's velocity with respect to the wing, and as a result drops it's pressure. Thus there is a low pressure region on the top of the wing compared to the bottom of the wing and as a result the airplane wing generates lift. In our hurricane model the increase in velocity due to the storm's rotation further drops the air pressure, and causes the storm to further increase in strength.
The multiple forces acting in synergy to drop the air pressure at the center of the storm causes the density of the air, or weight per volume to decrease. As we know, light fluids float on top of heavy fluids like oil floats on water, so the low density, low pressure air in the center of the storm begins to rise. A column of low pressure forms at the center of the storm and rises rapidly, further decompressing due to altitude change, and dropping further amounts of water vapor as it does so.
As the air "spouts" from the eye of the hurricane it then spreads back out, but this time it is heading in the opposite direction, that is from the center out, so that the Coriolis force we mentioned before acts to spin this high altitude air in the opposite direction. Thus, if you look carefully at the satellite image of a hurricane, you will notice that it is spinning counter clockwise at low altitudes, but spinning clockwise at high altitudes. This is actually something that we would not ordinarily expect, at lease from our traditional view of earth processes, and demonstrates the importance of the Coriolis affect when viewing and understanding large scale atmospheric and oceanographic processes like a hurricane.