This travertine is highly polished but you can see texture and duller areas on the tiles. This is due to different densities and composition within each tile. A product of Mother Nature, some contrast in shine can be expected.
Travertine floor with dull patches that are deep etch marks. Etches, or dull spots similar to these, are caused by acid reacting with the travertine. The acid eats the travertine, roughing up the surface of the stone. This can be caused by improper cleaning products or anything containing acid, such as lemonade, wine, or vinegar.