Pressure Gradient Force
Air is set in motion by a force known as the pressure gradient force. According to the laws of thermodynamics, air flows from areas of high pressure to areas of low pressure. The greater the pressure gradient, or difference, the faster the air, or wind, moves. This is nature's way of seeking a balance, or equilibrium. This is the same principle that causes hot chocolate to cool and an ice cube to melt when combined. Heat is transferred from an area of excess, the hot chocolate, to an area of deficit, the ice cube. The final temperature is a balance between the two original temperatures. In the case of the weather, it is nature seeking a balance between atmospheric pressures that generates the wind.
Pressure Systems
In nature, large areas of high and low pressure develop due to the unequal heating of the atmosphere. In high-pressure systems, the air is cooler and denser than the surrounding air. As a result, the air sinks. In low-pressure systems, the air is warmer and less dense than the surrounding air. As a result, the air rises. In nature, air flows out from sinking high-pressure systems, areas of excess pressure, and toward rising low-pressure systems, areas of deficit. This air flow seeks to replace the void left by the rising air and to create a balance.
Wind Speed
Atmospheric pressure is represented on weather maps by lines, called isobars. Like lines of elevation on a topographical map, these lines of pressure help to visualize the pressure differences in the atmosphere. The closer the lines are to each other, the steeper the pressure gradient. This gradient is like a ski slope. The steeper the ski slope, the faster a skier will go. Likewise, the steeper the atmospheric pressure gradient, the faster the air moves.
Differences In Wind Speed
Low-pressure systems, represented by a red "L" on weather maps, typically have very steep pressure gradients. This is why it becomes more windy as a low-pressure system approaches you. Conversely, high-pressure systems typically have very shallow pressure gradients. This is why winds are typically light and variable when an area of high pressure builds over your location.
An Example of Wind Generation
Imagine a balloon filled with air. Inside, the air pressure is much higher than the air pressure outside the balloon. If the balloon was to develop a tiny hole, the air would begin to leak out, moving from the area of high pressure inside to the area of low pressure outside. If you placed your hand over the leak, you would feel the air moving as wind. This is exactly what happens on a much larger scale in nature when air moves from areas of high pressure to areas of low pressure, creating wind.