The Preview panel gives a quick visualization of the active material and its properties, including its Shaders, Ramps, Mirror Transp properties and Textures. It provides many useful shapes that are very useful for designing new shaders: for some shaders (like those based Ramp colors or a Diffuse shader like Minnaert), one needs fairly complex or specific previewing shapes to decide if the shader-in-design achieves its goal.
One of the keys for the rendering of a good scene relies on the appropriate choice of the material properties of objects within it. You can have the most beautiful, the most original and the finest models of the world, poorly managed materials can nothing but spoil your scene.
It is important to understand how work the many Material Buttons in order to use them the best possible way.