Composition in artwork is extremely important. This is the structure of your image, piece of music, writing, etc. Often, if an image doesn't have an appealing composition, I barely even glance at it.
Some ways to create a better composition include: changing your viewpoint, using the "rule of thirds", limiting your focus (photography), or removing everything except your subject.
Viewpoint: change the way you look at something.
at an angle and looking up
down on the ground
Rule of Thirds: this grid is a setting found on most digital cameras under Display. The "rule of thirds" makes the artist aware of the location of the subject. The viewer will find these images more interesting.
Limited Focus: for close-ups, use the Macro setting that looks like a flower on your digital camera.
Minimal: this can really make the subject stand out.
Try some of these out next time you're snapping photos.