Why do shaders have a normal input? It is probably a very stupid question but why do have many shaders (diffuse, glossy, ...) a normal input ? What happens with that normal input ?

Maybe it helps when I clarify the background of my question...I am trying to understand the concepts of Physically-Based Shading and the implementation of these concepts in Blender. See also my questions here and here. 

After some discussion with @piegames I noticed that I do not really understand why the normal input is used in shaders. I think I understand what a normal is but with the concept illustrated below I have difficulty to understand what Cycles does with this normal input when calculating the behavior of a shader
A face normal is the angle perpendicular to the face, it is used to determine reflections and lighting on the face.

A normal map is used to visually deform the surface of an object. It does this by altering the face normal for every position on the face. This fakes extra detail by altering the rendering calculation without using extra geometry.

This is where the normal input comes in, by feeding a normal map into the node you allow blender to calculate the surface colour at a given point using the modified normals and not just the one face normal.

You may find Blender Gurus recent tutorial on photorealistic wood of interest.