Generally, the picture should be taken in a way that makes the subject the first thing which is seen in the photograph. Your subject should be the primary point of focus and should be crisp and clear. Ideally, there should be nothing in the photograph that draws more attention than the subject itself.
If, for example, you were to photograph a beach scene with a lighthouse as your subject, and a viewer is more drawn to a sandcastle on the beach, you've done a poor job of making your subject clear.
Obviously, there can be, and many times are, multiple subjects in one photograph. In this case, the objective is to obtain harmony and balance between all subjects. Do you want them both to be equally attractive, do you want one to pop while the others are slightly more subtle? These are all questions which you must address, and plan accordingly.
When choosing a subject, don't look at the photograph as the photographer, look at it as another photographer critiquing your work.