This sort of damage is common with wooden floors, particularly with softer woods, but is also becoming more apparent due to new finishes being clearer and letting the wood colour show through.
As for repairing the wood, you could try and find a colour filler that is roughly the right colour, both BonaKemi and Ronseal make them and they can be blended to get roughly the right colour. Personally I think your floor would look worse when you had finished though. I have heard talk of people using cool steam irons to expand the compressed grain, but as I have never tried it, and I am sure you would probably melt the surface lacquers before you achieved anything, I could not recommend this.
You could re-sand and re-seal but this will expose fresh unhardened wood fibres that will get damaged in the same way again.
Sanding and then re-sealing with Traditional Pine oils might be the best route. These oxidise in the top few millimeters of the wood and harden the surface of the wood. Its by no means bullet proof but it could be stronger than you have at the moment. I have used it on dance floors (admittedly with hard woods) and it has been very good. Look up Carls 90 oil on the internet
Resins are mixed with the finest and cleanest sanding dust produced from the floor being sanded. Many contractors I know keep spare dust marked up with the species. This is then applied into the damage or more commonly the joints before final sanding. The fillers mentioned previously are like a coloured "polyfiller" and fulfil the same role. The problem with either these or resins is that you will never get a 100% perfect colour match. The result will thus look very artificial (in my opinion)
That said it can be done sympatheticly by using a number of shades of colour and it is the only way of restoring a floor without resorting to sanding the wood.
Please be aware that which ever method you use they will both require re-sealing with a recoat of your current floor finish.