As for the texture maps...
Diffuse is the base color map of your texture, and it is lit by a dot product and does not take into account the perspective of the viewer.
Specular is a texture map that defines how might light is reflected back to the viewer when viewed at the correct reflected vector of the light source.
Specular exponent defines how rough or smooth a surface (or in this case, pixel) is. This is to emulate varying surfaces which may be matte, semi-glossy or glossy.
As seen above, a diffuse (rough) surface will scatter light in every direction, while a smooth surface will only reflect light at certain angles. It is common to see highly reflective surfaces to have a dark or entirely black diffuse, and a bright specular map.
Diffuse, specular and glossiness are all outdated and antiquated, if possible it would be more beneficial to learn PBR. PBR is easier to understand, more accurate, and has real-world values for different materials.
The old diffuse/specular shading model required a lot of tricks and trial-and-error to get textures to look correct, and even then wouldn't look consistent across different lighting environments due to how they approximate lighting.