The idea behind the global warming theory starts with the sun, which warms the Earth's surface with sunlight. That heat is then released back into space as infrared light, though some of it is absorbed by the atmosphere and sent back down, which keeps the Earth warm. Without an atmosphere, our world would be more like the Moon, in which day and night are scorching hot and freezing cold.
Some gases, like methane and carbon dioxide, do most of the heat absorption/keeping it on the Earth. There is some concern that if we get too much of these gases, then the atmosphere would store too much heat. At first, we thought this would mean that the Earth would eventually bake id global warming went too far, and we would all die. Before that, though, the ice caps would melt and also flood coastal cities. Now, however, we know that this is only one of many possible cases for global warming. Another thing that can happen, is that the extra heat can warm the oceans, causing water to evaporate. This vapor can then rise up into the atmosphere and cool as extra rain. The result in this case, is that we would have more hurricanes and the ones we have would be more powerful. The melting ice caps can also disrupt the way the ocean keeps certain parts of the Earth warm, and cause currently livable parts of the Earth to suddenly freeze in a new Ice Age. On the flip side, some argue that the extra rain and warmer temperatures may be a good thing, if they result in non-livable land becoming inhabitable by humans.
The bottom line is, we don't know *exactly* what is going to happen if we produce a lot of CO2, but many scientists would argue that there's a good enough chance that we could, in fact, make much or all of our planet un-livable for humans. Since the problem is so radical, along with the solutions, any attempt to reduce carbon emissions or even the theory of global warming itself is going to be controversial.