As far as I know, SR4 uses 3 texture files; diffuse, normals and specular maps, but only some things actually use specular maps. Whether you can change that or not I don't know.
Diffuse is your texture file, where you generally design the look and feel of the texture, add colours and so forth.
Normal is your lighting file, that simulates the appearance of concave and convex surfaces, bumps etc. (it's the funky looking purple texture).
If it does use specular maps, then they would control exactly how much light a surface will reflect (how shiny it will be).
I found a nice tutorial from YouTube on how to work with Saints Row 3 normal maps (with Photoshop); the same more or less applies to Saints Row 4 it seems.
It doesn't tell you how to do good normal maps, though, as I think that's something that comes from experience, just like all graphic work really. (could also probably find a tutorial or two on hints and tips for normals on Google).