Why are some of the boards in my hardwood floors disintegrating?
Its either rot or termites.

The discoloring suggests a water leak that persisted long enough to rot.  Do you have access under that spot?  Is the subfloor similarly discolored? If so, it may need to be repaired at the same time as the board.

Board replacement is possible by any flooring contractor by sawing out the center of the board and chiseling/prying out the side pieces.  The replacement piece will be dropped in by cutting off the lower half of its groove (of the tounge/groove pair) and glueing it in.  Small finish nails can also be used to tack it down (and set and filled with colored wood putty).

The new piece may be a bit proud if the floor has been refinished more than once, and can be presanded to blend.  

Here's a video found by Shirlock Hoimes on the TOH site