When composing a shot it's easy to focus all your attention on the subject and let your mind tune out the distracting elements in the composition. Unfortunately, those distracting elements will be very noticeable when you get home and bring the photo up on a computer. Those things you never noticed can ruin a photo.
Here's a recent example. My dad grows Orchids as a hobby. While visiting this last week I took a few minutes to go into the yard to see what I could find to shoot. This bloom was particularly pretty, but a good spot for an Orchid to grow is a bad spot to photograph it. There was a wooden fence and the bright wall of a neighbor's house behind it as you can see here.
I was shooting with a 300mm telephoto lens that I stopped down to f/4 to minimize the depth of field and blur the background as much as possible. In this case the flower and the fence were too close together to blur the fence enough. The solution was to get low and shoot up at the flower. By doing this I was able to take the fence out of the picture and just have the neighbor's house in the background. The house was much brighter than the flower so I exposed for the flower, which made the wall appear to be solid white, which is a pretty nice background in this case.
I think the second shot is a more pleasing composition. Anyone looking at it will look at the flower and not be distracted by the background.
The background is not the only thing to watch out for when composing your shot. Watch of objects that stick into the photo from the bottom, top or sides that can be distracting. In the shot below the railing for the bridge I was standing on was included in the lower left corner.
In the last example a cut log is showing up in the bottom of the photo. It was actually the remains of an old bridge but does not seem to fit in the forest scene and should be eliminated. Sometimes you can eliminate a distracting element by picking it up and moving it. Other times, you have to move yourself and recompose to eliminate the distractions
The best thing to do when composing is to slow down and look. Move around and see what other compositions you can come up with. Finally, watch out for the background and other things that can distract from the main subject.