What caused the discoloring? We're they ever sealed properly? Beautiful floors! If not sealed or not sealed properly you may have to bite the bullet and have them sanded and refinished.
What a gorgeous floor. You can a magic eraser to get the stains out, or if not sealed get a matching stain, and apply. You may have to sand the entire floor and restain.
Cathy, try using Murphy's Oil Soap, it's just for wood, it's an oil you can use to mop the floor. Follow the directions on the back of the bottle. Then use Rejuvinate to coat the floor, which will give you a nice shine. The oil is in the supermarket, and Rejuvinate at Home Depot or Lowe's.
Fading could be from spills, sunlight, and not properly sealed. Try using Bona for hardwood floors. Otherwise they may need to be lightly sanded, stained if you choose, and sealed.
Looks like something spilled on them. We clean our wood floors with 1 cup white vinegar, drop or two of Dawn and 1/2 cup alcohol (helps to dry faster) with warm water. Don’t soak the wood. And then we dance on old bath towels to get them a bit drier and it helps to buff them to a little shine. If they’re not sealed with some type of poly, use pure tung oil to seal them.
Use sand paper to remove the colour change from this area about 1 sq. meter. Apply a slight darker tan varnish where you have removed the entire markings from the floor area so as to match. If it appear still too light apply another coat again till it matches. Take your time to dry properly. Do a small areas to get the correct tan application!