Basic photo composition is very easy to learn and can take an average photo and turn it into something that's much more interesting!
The Rule of Thirds says you should take your photo frame and make mental lines disecting your frame into thirds, both horizontally and vertically:
If your subject is horizontal (like a landscape), your horizon line would be on one of the horizontal lines, and NOT right in the center. It just makes for a more interesting photo:
If your subject is vertical (like a person standing, for example), it should go on one of the vertical lines:
The subject in the photo below is actually the bee. The bee is roughly where a vertical and horizontal line would intersect, making the photo less static.
Now go out and take some great photos!