Clouds are made primarily of water droplets and ice crystals floating in the sky. They play an important part in the Earth's weather, and influence, and are affected by, the Earth's climate (see climate vs weather explaining the difference).
Figure 1. High wispy clouds reflect little sunlight, while trapping infrared radiation and warming the Earth.
Figure 2. Low thick clouds primarily reflect sunlight and cool the surface of the Earth.
Since clouds affect the climate, which in turn affects cloud formation, it is very important to study cloud patterns in the atmosphere in order to better understand climate change.
Clouds also play an important part in the water cycle, transporting water throughout the atmosphere to be deposited elsewhere. Visit Hydrologic cycle for more information.
A cloud's high albedo introduces a negative feedback to the Earth's climate. As the Earth warms this effect reduces the effects of the initial heating. Upon heating, more water evaporates resulting in greater cloud formation, which increases the total albedo of the Earth and reduces the amount of incoming sunlight that gets to the Earth's surface. This cycle plays a large part in maintaining the stable temperatures of the Earth, much like the human body sweats in order to maintain its temperature.
Certain clouds, however, absorb more outgoing sunlight than other clouds (see figure 1), resulting in less heat leaving the Earth's surface. The wispy clouds high in the sky act as a blanket, trapping in the light that the Earth would otherwise be re-emitting into space.
Satellite studies are still ongoing to determine the effects of clouds on the global climate, as their heating and cooling properties are very difficult to pin down.
The video below is a lecture from Prof. David Archer, Department of Geophysical Sciences at the University of Chicago, talking about how clouds affect the Earth's climate: