Repairing solid hardwood flooring typically means sanding and refinishing. If your floor is prefinished from the factory, contact the dealer or the factory to find out how to repair the finish -- or even if you can.
For deeper damage, consider replacing the problem strip or plank. If tongue-and-grooved that means drilling holes in the board, then cutting and chiseling out wood from the center as to not damage the adjacent boards. Then cut off the tongue of a new board of the same size and insert it in the hole. Finally, nail the board in place as you did the first row of boards against a wall.