Earth is kept warm by gasses in our atmosphere called "greenhouse gasses". Think of them as the blanket for our planet, since without the Earth would be much colder than it is right now (almost 60 degrees Fahrenheit colder!). The most important greenhouse gas in our atmosphere is water vapor, followed by carbon dioxide, methane, and a few others.
Basically, global warming is caused by increasing the amount of these greenhouse gasses in the air--the most important of which is carbon dioxide (CO2). CO2 is released any time we cut down a tree or burn a fossil fuel. Fossil fuels include coal, oil, and natural gas, all three of which are our main sources of energy. Every time you use electricity or take some form of transportation, chances are you are using a fossil fuel for power.
For many years we have been burning more and more fossil fuels, and this has caused more and more carbon dioxide--a greenhouse gas—to be released into our atmosphere. Most scientists believe it is this increase in carbon dioxide that has caused the planet's average temperature to rise over the past 100 years.
So why does this matter? Well, if we continue to burn these fossil fuels it could cause the planet to continue to warm, and no one can say for sure by how much and how fast it will warm. But it could be very large and very significant--as much as 5-6 degrees in as little as 100 years (it does not sound like much, but consider that during the last ice age temperatures were only about 5-6 degrees colder!)
The effects of such a drastic and rapid rise would be devastating. Sea level rises could destroy coastal cities and displace billions of people, agriculture could completely fail as precipitation patterns shift and desertification takes hold, rivers could run dry as the mountain glaciers that supply them melt and/or stop receiving snow. Diseases can spread by mosquitoes (which depend on hot temperatures). The effects go on from there.