Well, Erickson et al (2011) attribute the increase in brain volume in the aerobic exercise group to brain-derived neurotrophic factor (BDNF).
Specifically (p. 3020):
> In fact, we found here that changes in serum BDNF levels were associated with changes in anterior hippocampal volume; an important link because the hippocampus is rich in BDNF, and BDNF levels increase with exercise treatments in both rodents and humans. BDNF is a putative mediator of neurogenesis and contributes to dendritic expansion and is also critical in memory formation. Our results suggest that cell proliferation or increased dendritic branching might explain increased hippocampal volume and improvements in memory after exercise
with the caveat:
> however, increased vascularization (15, 16, 33) and dendritic complexity (34) may also be contributing to increased volume