Here are a series of articles and videos that talks about the Rule of Thirds.
The rule of thirds is one of the most fundamental guidelines in photography, if you know about the concept, it will easily help you make better images. The concept proposes that an image should be sub-divided into nine equal squares by having 2 horizontal and 2 vertical imaginary lines equally spaced, and the objects of the image should be placed along these lines or along the intersection of these lines.
Image above from rule of thirds wikipedia page
This video is from B&H Event Space seminar, David brommer looks into Beyond The Rule of Thirds by touching on many different aspects of photographic composition.
Additional Resources about Composition which include rule of thirds to read.
One of the first questions to ask yourself when composing your picture is: “What is my subject?” Of all the things you see in front of you, which one is the reason for taking the photo? Once you’ve answered that question you can begin to work on how best to show that subject. The rule of thirds is a guide to help you do just that.
This rule of photography applies to much more than landscape images â€“ it also applies to portraits. When framing a tight crop of a portrait, many new photographers will place their modelâ€™s face dead center. However, when we look at a portrait we typically are drawn to the eyes as the focal point â€“ this means that if we follow the rule of thirds, we should place the eyes on the top third of our image â€“ this makes for a more balanced photo.