I remember (vaguely) something from a health class in 5th grade where the nurse was describing how these cells "scrub" foreign particles from the tissue of the lungs, and that the more you smoke the less able they are to keep ahead of the tar you're building up...
My undergrad anatomy prof described something similar. Basically, the cells that line your lungs secrete mucus to protect itself from foreign stuff (e.g., bacteria, viruses), and they also have cilia that move autonomically in such a way as to move that mucus (with the bacteria and viruses, etc., it caught) up and out of the lungs. Smoke causes the cells lining the lungs to retract the cilia, so that junk caught in the mucus, and the mucus itself, is not removed as efficiently. It requires very little smoke to cause retraction of the cilia, and it takes about 3 months for them to re-extend, so in this way, one cigarette a day is similar to a pack or two a day. BUT that's not the same for other, e.g., cardiovascular effects of smoking.
I have a hard time believing that it took 15 years for his lungs to fully recover. The damage to the lungs should take months, not years, to recover, but that isn't necessarily true for other systems in the body. I think it is more likely that he took up jogging 14 years after he quit smoking and only then realized the full benefits of quitting.
disclaimer: I have not thoroughly evaluated the primary literature--I have only a textbook knowledge of this.