The greenhouse effect is a natural process and it's effects are both good and bad for us. Carbon plays an important role in the greenhouse effcet because carbon is found in carbon dioxide, which is one of the greenhouse gases. A greenhouse gas is a gas that absorbs infrared radiation. Other greenhouse gases include water vapor, nitrous oxide, and methane.
What happens in the greenhouse effect is simple. Heat (infrared radiation) from the sun that is released from the surface of the Earth is captured by greenhouse gases like carbon dioxide. These gases trap or redirect the heat back to the surface. Thus, the temperature always stays relatively warm and continues to rise slowly.
In one way, what happens is good for us. The temperatures brought on by the greenhouse are effect are just the right mix to sustain life on Earth. The flip side is that these temperatures are steadily rising and the Earth is becoming warmer by the year. This can lead to global warming and melting of the poles. The melting can cause rise in ocean levels and cities can become flooded. This may be way off into the future and global warming may have slowed down by then, but it would still be a major problem.
The major contributers to the greenhouse effect are deforstation and consumption of fossil fuels. Deforestation turns the carbon in the living tree into carbon dioxide when the tree dies. This carbon dioxide is released into the air increasing the number of greenhouse gases and the greenhouse effect. Burning fossil fuels (for gasoline and from factories) also releases a significant amount of carbon dioxide into the air.