The rule of thirds is an invisible guideline that consists of two horizontal and two vertical lines equally dividing the frame in 9 pieces. When placing an element on any of these lines or intersections we seem to have a stronger layout and create more visual interest in most cases.
I say most cases, because sometimes in photography for example a centered portrait shot may be more powerful than having a non symmetrical image.
Understanding proportion and various elements of design are guidelines only and you should always follow your instincts combined with your knowledge, try to experiment and try something drastically different.
That said many works of art have followed the rule of thirds and created a great visual interest for the viewer. Pay attention to these images, and how the placement of the tree and grass change the focus of the picture. When the tree is on the 1/3 or 2/3 of the frame it has more dominance and importance. Even with the tree/ sky balance the meaning of the image changes.
If you take a photograph of the beach and ocean and you frame the water and sand 50/50 it won’t be as interesting as framing it 30% sand / 70% ocean or 70% sand / 30% ocean. Or in this case the sunflowers.
The placement of the elements in a frame may have a strong role on the meaning of the element.
Which one do you like more? Which one is more successful?