Composition is the art of placing objects inside the four sides of the picture. The picture above is an example of what not to do. Take a look at it and try to figure out what is wrong.
The rule of thirds is the most basic tool for good composition. All it says it that the composition area is divided into nine squares. Think of The Brady Bunch to get a visual picture. Place the subject anywhere except the center square. The subject can be at the top, bottom, left, or right third of the picture. In this picture the subject is placed more towards the bottom third, so that's good.
As more people have access to quality cameras, everyone is a photographer. As good as today's equipment is (including todays cell phone cameras), the camera cannot compose the picture. The picture above fills the frame. That's what everyone wants, right? Unfortunately that is not always correct. People tend to zoom in and crop as close as possible. The foreground and background help to put the subject in context and tell the story. There is nothing but subject in this picture. What is being missed? But that's not the biggest problem.
What happens to this picture when you decide to have it printed? If any print size other than something that is a 2:3 ratio is chosen, the subject will be cut off severely. As such only 4x6, 8x12, 12x18, etcetera will work. Look at the pictures on social media and you will see similar pictures everywhere. I actually see people displaying pictures of their car at car shows with both ends of the car cropped out. The second factor in zooming and cropping so close also affects prints. When the print is framed the matte or frame will overlap the edge of the print and cut off the subject at both ends.
Just like any other rules and guides, the rule of thirds can be and is broken frequently. It does work well as a reminder and helps keep the picture interesting. If a picture is well composed, people will generally like the work. If it's not well composed, people will not like it as well and most will not be able to you why. Composition can be aggressive or subtle, it depends on the subject matter and what the photographer wants the viewer to see. There is a lot more to composition than what I have talked about here, but this is the building block for everything else.