The author is likely referring to the mechanosensory behavior of bone (reviewed in Huang and Ogawa, 2010; lots of Google Scholar citations). Bone loading produces very tiny mechanical deflections (strain) which are translated into biochemical signals that promote bone growth through the action of osteoblasts. Burger and Klein-Nuland (1999) review possible mechanisms.
The low frequency soundwaves produced during purring overlap the frequencies that have been shown experimentally to induce bone formation (1-50Hz; e.g., Castillo et al., 2006; Xie at al. 2006). Although an interesting hypothesis, I don't think that osteogenesis in response to purring has ever been experimentally shown in cats.
Huang C, Ogawa R. 2010 FASEB J. 2010 Mechanotransduction in bone repair and regeneration. 24(10):3625-3632.
Burger EH, Klein-Nulend. 1999. Mechanotransduction in bone--role of the lacuno-canalicular network. FASEB J 13(Suppl):S101-S112.
Castillo AB, et al. 2006 Low-amplitude, broad-frequency vibration effects on cortical bone formation in mice. Bone 39:1087-1096.
Xie L, et al. 2006. Low-level mechanical vibrations can influence bone resorption and bone formation in the growing skeleton. Bone 39:1059-1066.