Mesmerism and related phenomena — the ability to induce states of trance, insensibility to pain, or heightened perception in subjects through the practitioner's concentrated attention — were widely discussed in Schopenhauer's time. Rather than dismissing them as fraud, he takes them seriously as evidence of a kind of interaction that cannot be explained by ordinary physical causality. If two people's bodies are expressions of the same underlying will, then direct influence between them — bypassing the usual sensory and causal channels — is exactly what the metaphysics of will would predict.
The philosophical import of animal magnetism, for Schopenhauer, is that it confirms the will's transcendence of the principium individuationis. The forms of space, time, and causality separate individuals as objects; but at the level of the will — the thing-in-itself — individuation is a secondary feature of representation. What we call one person's will and another person's will are, at the deepest level, the same will differently instantiated. Phenomena in which one person's will appears to directly affect another's body are therefore not violations of natural law but confirmations of the deeper unity beneath the law.
The chapter "Animal Magnetism and Magic" in On the Will in Nature was Schopenhauer's most contentious contribution to the discussions of his day. While the specific phenomena he cited have not been vindicated by subsequent science, the philosophical point — that the will, as thing-in-itself, is not bound by causal-representational categories — remains central to his system.