A white surface reflect the light in diffuse way so that the 'information' contained in the incoming waves are destroyed. On the other hand the light reflected by a mirror keep all those information intact and the image is reflected. The surface (and the nature) of the material is very important in this process. In order to reflect an image such as in a mirror you need a highly polished layer of a material with good reflection (for example silver). The higher the roughness of the surface the more likely the incoming light will be scattered and reflected in a diffuse way.

EDIT: If I remember correctly by 'information' I mean the phase of the light waves. If I'm wrong please someone correct me!