One of the hallmarks of Narayan's writing is that all of his characters, even those which play more minor roles in the story, are extremely complex. To this end the headmaster, a minor character, is still incredibly well fleshed out and dynamic. He is slightly peculiar—relying heavily on the predictions of astrologers and on ideas of omens. He has a similarly strange perspective on teaching developing his own methods and materials that, while not shocking, are unique and imaginative (while still being strictly rooted in traditions).
Ultimately, the character of the Headmaster represents someone who has been shunned from the world because of his traditional and spiritually rooted understanding but who nonetheless perseveres and manages to create a sense of community and solace for himself.