Wind
The circulation patterns that are seen in wind result from three major factors: solar insolation, density differences in air, and the rotation of the Earth.
The Role of Density
Let's take a look at the equator, the area that receives the most solar insolation. Warm air, along with holding more moisture than cold air, is less dense. This results in warm air rising higher in the atmosphere, where it begins to cool. As it cools, it loses its ability to hold as much water vapor, resulting in precipitation. As the air continues to cool, it becomes denser and sinks.
Along with this, air moves from areas of high pressure to areas of low pressure. If you've ever squeezed an open water bottle (applying pressure to it) and felt air come out of it, it's due to that same property. If you look at what we were just talking about above, there is one area where air is moving away from the surface, and one where it is falling towards the surface. Where the air is falling has a higher pressure, resulting in the air moving away from where it is falling.
Hadley cells form as a result of the heated air at the equator warming and rising, cooling and falling around 30° latitude, and then moving back towards the equator. This continues in a cyclical pattern of air circulation.
Not all of the air moves back toward the equator, however. Some will move towards 60° latitude, as it will also have a lower pressure than 30°. Around 60°, this air reaches air from the poles, which is colder due to the poles' lower insolation. As the air that was coming from 30° is warmer than the air it is meeting, it will rise and cool. Some of it will fall back at 30°, forming Ferrel cells.
Some of the air that rose at 60° will move to the poles before cooling and falling. After falling, it will move back toward 60°, where it will meet the air that was coming from 30°, forming a Polar cell.
It is in this way that the unequal heating of Earth is in a large way responsible for global air currents, and how solar radiation that arrives at the equator can be distributed throughout the planet. These patterns result in biomes being found at predictable latitudes. For example, the equator has warm, moist air and therefore you are most likely to find tropical rainforests there. On the other hand, the cool dry air falls at about 30°, resulting in deserts being found at this latitude. Please see the image below for a fuller picture of this concept.
The Coriolis Effect
If you've ever been eagerly watching the weather to see if a big snowstorm is coming so that you can get a snow day, you may have noticed that where we live, the weather comes from the Southwest.
If you've ever watched the best movie ever, Aladdin, you may have noticed that the song, "Arabian Nights" has a line, "where the wind's from the East" and then probably never imagined it would somehow become relevant in learning something for a science class.
What do the two of these have in common? They're caused by the rotation of Earth and the resulting impact on the wind, known as the Coriolis effect. If Earth was completely stationary, air would move horizontally from high to low pressure in simple, straight lines. But Earth rotates, causing deviations to that path and causing curved paths.
Earth rotates towards the east and it does so at a constant rate. However, the Earth does not have a uniform width - the equator is wider than the poles. Due to this, despite one rotation of Earth taking a day, a point at the equator has farther to go than a point at 30°, and therefore must go faster.
If the air is moving away from the equator, it is moving east faster than the land below it, making the air curve to the east.
If the air is moving toward the equator, the opposite happens; it is moving east slower than the land below it, making the air curve to the west.