Fossil fuels cause the "Greenhouse Effect". The Greenhouse effect is where gasses bounce off the Earth's ozone layer, and the Earth becomes, well, like a Greenhouse. Burning Fossil fuels produces different gasses, like CO2 (Carbon Dioxide). Our ozone layer, as mentioned before, traps in all of these gasses (it's main purpose is to keep heat in), and it causes heat, which bounces back off of the Ozone layer, and rebounds towards the Earth. Not all of the gasses do this though. Once the gasses reach the Earth, they warm the earth. Gasses also bounce off the Earth, although only some, and bounce back towards the atmosphere. The ozone layer bounces some gasses off, but lets some go through the layer. And the cycle keeps repeating.
Basically, Fossil Fuels create global warming.