Good composition in an image is like a well formulated thought. It's necessary for the viewer to really get a grasp on what you're trying to say with your image. Now, it can be argued what good composition is, because it is to some degree subjective, but there are some canons that we can begin with. One that many have heard is the "Rule of Thirds". This method is very traditional, very 'Old School' if you will, but mastering it is a mandate in your tool box of photographic skill sets. Once you understand the 'ROT' , you can be more conscious in how you choose to break this rule.
The Rule:
The image should be imagined as divided into nine equal parts by two equally-spaced horizontal lines and two equally-spaced vertical lines, and that important compositional elements should be placed along these lines or their intersections.
In this image, I have my subject falling on the left side of the frame along the line. Also, I attempted to use the actual buildings structural lines to fall along those same gridded lines to make somewhat of a frame around my subject creating a frame inside of a frame.
A similar situation can be seen with this image of Chrisette Michele. One major difference is I wanted her head to fall at the intersection of the lines in the top right hand portion of the frame, allowing her body to trail into the bottom left portion of the frame.
Keep in mind this isn't a rule that only works when framing horizontal images, it also can apply for vertical images as well.
In this image I put the eye specifically in the intersection of the lines in the top right.
Sometimes its also appropriate to have your subject fall into the center of the frame or heavy to the left or right without actually landing on the lines or the intersections of them.
The challenge is to really consider how you compose an image. Be sure to take care in where your subject lands in the overall frame. It will make your images come across more thought out and more professional. This doesn't mean you always have to follow this rule, but hopefully now that you know this rule, and how it can be applied, you can go back through and audit your own images. I'm sure you'll see that some of your most successful pictures follow this rule without you even noticing.