In another of my posts called What is ISO I talked about something called noise. This is the grainy effect you can see on your images in certain circumstances. Increasing the ISO setting on your camera is the main way that you will start to see more noise.
The following image shows 3 different ISO settings. These pictures were taken on my Sony Alpha 100, and the amount of noise you may see on other cameras may be better or worse than this. Try it for yourself with your camera so you can see how your camera performs.
You can see on the zoomed in areas that ISO1600 produces much more of the noise or grain effect than ISO100.
So when you are taking pictures, try to keep the camera on the lowest ISO setting you can as that will give you the best quality image.