"Teddy" explores different ideas in Eastern religious philosophy, focusing on reincarnation, Zen kōans (a.k.a. philosophical riddles), transcendence, detachment, and enlightenment. The story makes the point that living a spiritual life is very difficult in America, and shows some stereotypical American resistance to Eastern ideas. Main character Teddy maintains that it is the soul, not the body, which matters; therefore, physical pleasures and any sort of materialism are to be avoided.
A reader need not have any background in Eastern religions nor even grasp the nuances of Teddy's philosophical argument to understand "Teddy."
To understand "Teddy," a reader needs to be well versed in the religious philosophy Teddy discusses.