The rule of thirds follows the basic principle of dividing the composition into 9 sections to maximise areas of interests. Aligning a subject into the range of these areas will create a much more energetic and interesting composition. Often, the eye level falls on the top horizontal line with subjects intersecting the two vertical lines.
Here I have taken some screenies from Pixar's Wall-E to demonstrate this in practice. It certainly breathes life into some of the most basic and complex of shots, maximising their effectiveness on the big screen.
Its a good habit to pick up from and will certainly improve framing and composition in creating scenes.