Specular maps are the maps you use to define a surface's shininess and highlight colour.
The higher the value of a pixel (from black to white), the shinier the surface will appear in-game. Therefore, surfaces such as dry stone or cotton fabric would tend to have a very dark specular map, while surfaces like polished chrome or plastic would tend to have lighter specular maps.
The colour of a pixel is also used, to calculate the resulting colour of the surface. A very saturated specular map will have a very different visual effect than a grey specular map. If you need a more "neutral" highlight on a surface, your specular map should use the inverse of the diffuse map's colour. Using the same colour on the specular as on the diffuse will result in a more saturated highlight when viewed in the game.
You can use contrasts in specular to make a surface appear more visually interesting in the game - for example, this door has a very dark specular for the wood while the metal parts are much lighter, which will make the metal stand out more as a shinier surface when light hits it. This sort of contrast can help make surfaces in the game appear more realistic too.