In a sense, the earth is a big greenhouse. While we may not have a big glass dome covering the planet like an actual greenhouse, we have an atmosphere that serves the same purpose.

In an actual greenhouse - like nurseries use, for instance - the glass helps to capture the heat provided by the sun as it shines in through the glass. It's the same effect you see in your car when the air inside warms on a sunny day. Sunlight shining through the glass warms the air on the other side, and that air trapped behind the glass continues to warm as the sun shines.

The greenhouse "effect" is actually the reason we are here on this planet. Those gases allow the sunlight to warm the air enough so that life as we know it thrives. It's a balancing act though - if the layer of gases is too thin, the sun's heat isn't trapped, and we would freeze. Too much greenhouse gas, and the heat builds up too high.

There is an article on the PBS website for NOVA that I think provides a very simple & clear explanation of the "greenhouse effect."

The most abundant so-called greenhouse gases that make up our atmosphere are water vapor, carbon dioxide, methane, nitrous oxide, ozone, and chlorofluorocarbons (CFCs). Each one of those elements has a different effect on solar radiation.

Carbon dioxide, methane, and nitrous oxide are considered the main "greenhouse" gases in the atmosphere because of their abundance and effects on trapping heat. All three gases have increased in the atmosphere since the start of the industrial revolution. I found a good explanation of the greenhouse gases on the National Climatic Data Center website (which is part of NOAA, which in turn is a part of the US Department of Commerce). There is additional information through the World Data Centre for Greenhouse Gases (which is maintained by the Japanses Meteorological Agency in cooperation with the World Meteorological Organization). They gather data from dozens of monitoring stations located all over the planet, and analyze these data to evaluate changes in atmosperic levels of these gases.

When people talks about "carbon" in the atmosphere, what they are really referring to is carbon dioxide, CO2, which comprises about 25% gas in our atmosphere. The increase in levels of CO2 in the atmosphere can be directly tied to human sources that are primarily related to the burning of fossil fuels. The burning of carbon rich materials, like coal and oil, increases the amount of CO2 in the atmosphere.