To answer that question, let's focus on the Landsat Satellites which produce images that might be familiar to you, such as this one of the San Francisco Bay Area.
The Landsat satellite completely images the Earth from 81 degrees north to 81 degrees south every 18 days. Its orbit around the Earth passes over the poles, and is timed so that it passes over each latitude at the same time each day. The Landsat satellite orbits around the Earth from north to south, but the Earth also rotates from west to east underneath it, so each orbit cycle the satellite makes passes over a different swath of the Earth.
As Landsat passes over the Earth, the Thematic Mapper imaging tool collects light reflected off the surface of the Earth. It does not measure all of the light reflected, but passes the light through filters which break the light up into distinct wavelength bands. Each wavelength band is the optimum wavelength for discrimination of certain features, such as vegetation or water. For example, the infrared band is used to measure the portion of the electromagnetic spectrum which is invisible to us but which we feel as heat. This reflected energy is useful in discriminating evaporation in soils and minerals that contain water.
Landsat images do not appear in the colors we are used to -- vegetation, for instance, appears red in Landsat images instead of green. This is because normal vegetation reflects infrared and red wavelengths which are detected by the satellite. Normally our eyes don't see these wavelengths and we think vegetation is green. Landsat makes use of wavelengths of light that our eyes cannot see - that is part of its special usefulness to us.
Now that you've read all that, have a look at this schematic
diagram
of a satellite sensor, based on the operations of NASAs Multi-Spectral
Scanner, the predecessor of the Thematic Mapper. The Multi-Spectral
Scanner and Thematic Mapper are spaceborne remote sensing tools that
collect light and process it into pixels and images. Both the Thematic
Mapper and the Multi-Spectral Scanner work basically the same way, as
demonstrated in this diagram. 
Notice how the sensor is travelling south
over
the Earth, and the Earth rotates east underneath it. Light reflected
from
the Earth is collected and filtered, then sent to a data processor to be
turned into pixels assigned to a specific location. This in turn will
form
one of the thousands of images of the Earth that Landsat creates each
year.
Landsat images are a type of satellite image that you are likely to encounter in many applications, but there are a myriad of satellite sensors collecting other types of data on the atmosphere and Earth. These satellite sensors operate in much the same way as the Landsat sensors to catalogue atmospheric data, such as the ozone or sulfuric acid present in different levels of the atmosphere.
SAGE (Stratospheric Aerosol and Gas Experiment) II measurements of global sulfur dioxide after Mt. Pinotubo eruption, from NASA.
Other satellites use radar to map the topography of the Earth very precisely - these measurements are useful for measuring the ice at the poles, which allows us to follow global warming trends.
Radar Ice Sheet Map of Antarctica, from NASA
There are other satellite-based sensors that measure the ocean color to determine the amount of plankton in the ocean. Since plankton give off oxygen we can breathe and form the basis of the food chain, they are an important indicator of the health of the oceans.
Map of Baja California seasonal ocean color, from NASA
Some rocks show up very well on satellite images, but this depends on whether the rocks are exposed well enough to be imaged and if they contain minerals that reflect light in the wavelengths collected by satellites. In some cases, satellite data and radar data can be very useful for compiling geologic maps. Researchers in Germany found that satellite radar data was sensitive enough to detect offsets of as little as a few millimeters -- making it potentially applicable to studies of earthquakes and plate tectonic motions.
Not only can satellite data be used to detect air pollution and contaminants, it can be used to detect the release of some hazardous materials and can also be used to monitor oil spills on the ocean.
Vegetation reflects light in several bands and each type of vegetation reflects light differently from the others. This makes satellite-based collection of reflected light ideal for cataloguing trees and vegetation. This in turn can be used to find the extent of habitat for various animals.
In 1997 the CIA established an "Environmental Center" to monitor and forecast international trends that affect treaty compliance, environmental crises, or long-term environmental trends. For instance, the CIA realizes that water shortages in Gaza could affect stability in the Middle East and wishes to monitor environmental trends as a means of understanding and predicting political situations.
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