It is absolutely essential that you continue.
But to actually answer, Stanley Milgram was a psychologist who wanted to know about obedience to authority. He was interested in this after the Nuremberg trials where a common justification for the crimes committed was “I was just following orders.”
He set up an experiment where participants had to administer electric shocks to another participant if they made an incorrect answer in a learning task. Each time they gave a shock the next one would be increased up until the final level of “Danger: Severe Shock”. A majority of people complied in giving this essentially lethal shock to a stranger.
In reality the shocks weren’t real, the participant receiving them was in another room and was an actor hired for the experiment. Still many believed they had actually hurt someone.
Edit: forgot the take home message. A lot of the participants didn’t want to proceed with harming the other participant. When they expressed concern and wanted to stop, the experimenter, seated in the room with them, would tell them things such as “the experiment requires that you continue.” This was the main point, that having someone in a position of authority (here the experimenter) telling someone to do harm to another was “enough” for many to continue.
Wikipedia has a solid write up on it.