A specular map displays the parts of a model that will reflect light in a certain way. If you had some scratches on metal, you could use a specular map to influence the shininess of different areas.
Normal maps are like bump maps, except they work using more info. That's a really simplified explanation, but I think it's correct (?).
Dirt? No idea, I think dirt usually gets added just in the texture and bump maps.
Of these, I think specular is important if you want the shininess of your model to be unevenly distributed. Normal maps are important for game models I think, or basically if you want increased detail without adding too much geometry, like a bump map. Hope that helps.