The element of a volcanic eruption that could have the most far-reaching impact on humans, up to hundreds of miles away, is the shock wave. Shock waves can travel great distances and can affect areas far from the eruption site, causing damage and influencing the environment in ways that can impact human populations.
While pyroclastic flows and lava are extremely destructive, they typically affect areas much closer to the volcano. Magma, being underground, does not have a direct impact on the surface environment until it erupts.