Responsibility was a duty or obligation that someone had towards others or towards the tasks they are assigned.
In 2254, as a captive of the Talosians, Captain Christopher Pike expressed his frustration with the situation by throwing himself against the wall of his cell. Later, when he was experiencing an illusion of being back home in Mojave with Vina, Captain Christopher Pike recognized it as an escape from reality. It was a life free of responsibilities and frustrations. (TOS: "The Cage")