What is composition, anyway? Before striving for any goal, it's a good idea to define that goal clearly. So, before you can achieve good composition, you need to understand what that means.
A photograph is a collection of visual design elements arranged within a frame.
The visual design elements include light (and its constituent parts of color and brightness), line, shape, texture and perspective.
Composition is the deliberate arrangement of these design elements in a pleasing or compelling manner. Learn some photography rules of composition that are really guidelines to effective arrangement of visual design elements.
In contrast, a snapshot is the result of just clicking the shutter without forethought or planning. The difference is one of taking a photograph, versus making it.
© Julie Waterhouse Photography
Picture composition is important in photography because a good composition can strengthen the message the the photographer is trying to convey in the image. it's often difficult for a non-photographer to understand why a photographer is taking so much time to take a picture. "Hurry up and click the shutter already! What are you waiting for?" Have you heard that from your friends? I have. And now I try to travel only with other photographers ;-)
Taking your time is import and worthwhile. It allows you to carefully consider your composition, and fine-tune it to include only those elements that contribute to the intent of the image, and to arrange the elements within the picture space in such a way as to maximize the impact of the image.
Using a tripod can be helpful to improving your picture composition. It holds the camera steady, while you make careful adjustments to the framing of your image. If you are shooting a stationary subject, I always recommend using a tripod for this very reason. It lets you slow down and be deliberate about your framing of the image. Read more about framing your image in the section on cropping photos.
Next, you may want to visit the first of the visual design elements pages about light.