Everyone is suggesting that the floor was stained and then had a finish put on. I suspect that what you are looking at is 3/4 inch tongue + groove (T&G) red oak flooring that has had an oil-based polyurethane finish. This finish yellows and darkens as it goes on and further yellows and darkens with age. In the first photo, you have a section of floor where the finish has worn away with repeated traffic - probably not just feet, but moist feet. In the second the cabinet covered a section of the floor that is not quite as yellow and dark as the rest probably due to less sunlight or oxidation or something.
I think you could cheaply try using a palm sander and feather in a patch for the first section by sanding to new wood in the worn section and over 6 - 12 inches out sand the through the finish to lightly sand the rest. After throughly dusting, paint on some oil-based poly and see if you get a live able solution. If it does not work, you will have spent <$50 for the poly and the sand paper. If it partially works, you will have protected that section of the floor and it will look a little off.
As mentioned above, if the floor is thin, (look for nail heads starting to show through or sections of tongue breaking off), then you will need a bigger repair. It still can be a DIY job, but slightly more involved.
If you decide to redo the floors, I would suggest you NOT use oil-based poly, but instead investigate a water based finish. It is a completely different look, but it lasts and lasts at least 3 x longer then oil based- especially in a wet area like this door way.
Best wishes, Ap (I did 2000 sq ft of T&G red oak myself and finished with Traffic by Bona).