Upon repeat damage to the microstructure of bone, cells called osteoblasts are recruited to the site of "injury" to trigger a large cascade of actions. First, osteoblasts secrete chemical signals into the blood to recruit another cell type, osteoclasts, which are related to white blood cells in lineage. They break down small parts of the cortical bone surface around where the break happened. Then, the osteoblasts act to deposited new bone onto the gap created. The result is called an osteon, which is like a cylindrical sheath of new bone. This serves as the major structural improvement of the bone, giving it reinforced strength along the general axis of the initial break.
Actual changes in bone mineral density are a lot of systemic, and rely on osteoblasts to be able to deposite more hydroxyapatite (calcium crystal) into the collagen matrix that is bone. We don't think this is as relevant in cortical remodeling as it is in development (such as osteogenesis imperfect a, the disease Samuel L Jackson had in Unbreakable). Bone mineral density is also the enemy in osteoporosis.
As far as desensitization to pain, it's probably due to destruction of affront sensory fibers along the area of contact. Interesting thing, though, is that bone is heavily populated by nerves, and some of these are actually from the sympathetic nervous system, which has been recently discovered to have a major role in bone remodeling. Whether these nerves remain in tact or all nerves are lacking after such training has yet to be studied in a controlled animal model.
