This is an excellent question, one that many scientists and others are concerned about. It is such a popular topic that I found many resources on the World Wide Web that discussed this issue. Try some of the links at the end of this question to see how much is written about this topic!
The Greenhouse effect is a process that is naturally occurring on our planet. The reason it is a concern is many scientists believe the process is being changed because of our use of energy in the last 100 years or so. This is how it works: the sun's radiation (think of the hot sunbeams on a sunny day--but the sun radiates energy even when it is cloudy or dark) travels through space to our planet Earth. When this energy hits the earth, the earth in turn reflects that energy back toward the sun (think of a light shining on a metal surface). But the earth has an atmosphere--it is surrounded by a shield of water vapor, carbon dixoide and other so-called "greenhouse gases." The main greenhouse gas is water vapor. These greenhouse gases trap some of the outgoing energy and keep it in, warming our planet up to temperatures that we can live in. If all the sun's energy was radiated back out into space, our planet would be like Mars--cold and lifeless. The greenhouse gases also function to reflect some of the sun's radiation away from out planet, so it does not get too much energy from the sun. Not all the sun's energy that comes to earth is kept in--a fair amount of it goes back out into space.
So why are these gases that make up the atmosphere called "greenhouse" gases? Think of a glass greenhouse where plants are grown--or perhaps you have seen a terrarium, which allows the sun's energy to come in and then keeps it in to make the inside air much warmer and more humid than the outside air. Scientists remind us that a man-made greenhouse does not really work in the same way that the earth's greenhouse effect does (the greenhouse is not really radiating energy back, it is just trapping the sun's energy with glass by not allowing the energy to escape).
The important thing to understand about the Greenhouse effect is that there is a delicate balance of the amount of energy that comes in from the sun, compared to the amount of energy is reflected back out into space. This balance of some energy in, some back out keeps the climate of earth stable so we can live. Scientists know that the temperature in different places on the earth varies very much, but they are concerned with an average temperature for the whole surface of the earth, which stays the same over time. Right now, the average temperature of the earth is about 15 degrees celcius. The atmosphere, consisting of clouds, gases, wind and other things keeps the temperature regulated so life of all kinds can flourish.
The problem comes when we add more greenhouse gases--especially carbon dixoide, nitrous oxide, and methane--to the atmosphere. We add these gases by burning fossil fuel (gas, coal) using aerosol sprays, and from other sources. Greenhouse gases absorb and hold in the sun's radiation. Because we have added more gases in the atmosphere than there would be naturally, some energy that should be reflected back into space towards the sun gets trapped and may cause the average temperature of the earth to rise. This is called "global warming." Even a change of half a degree hotter in the average temperature can make all kinds of changes to the oceans and the land on earth. Remember, it is not local temperature that matters--it can be boiling hot in the summer or freezing in the winter, and that is not "global warming (or cooling)."
So when people say they are worried about the "Greenhouse effect," they are worried that an increase in the amount of gases we produce are going to allow the earth to warm up a little bit all over, which can cause major changes in the climate of the earth.
Scientists agree that there are more greenhouse gases in the atmosphere than there were before but they do not agree on how that will effect the earth. Some scientists think the greenhouse effect will effect the earth a lot by changing the climate--but they are not sure how long it will be before the climate changes. Other scientists think that the earth's climate systems will fix themselves. Some worry it may take a long time to do this (hundereds of years.) So your question, "what is the greenhouse effect," is actually a question that lots of scientists are asking, and no one really knows what the long term outcome will be.--Mindy Basi