[frayesto]

The reason it's showing those interesting paths is because it's plotting the relative motion of the planets with respect to the Earth.

So visualize the moving Earth in the center of each image with the other respective planet moving relative to the Earth. Since both are moving and rotating about the Sun we get these interesting motions with a lot of structure.

This is the theory of epicycles which was the main theory of the motion of the planets before the heliocentric view became prominent.