Imagine that you are on a trolley that is barreling down the tracks extremely fast towards six people who are tied onto the tracks. Now imagine that there is a lever on your left side next to you and that lever makes the train switch onto another track which only has one person tied to that track.
You can then either pull the lever, switching the trolley onto the other track that only has the one person tied to it, killing the person. Or you can do nothing, allowing the trolley to kill the six people.
The Utilitarian would say, "I switch the trolley to the new track, because it's better to kill one person than to kill six." The non-utilitarian will say, "I leave the trolley to kill the six, because at least then I am not morally at fault."
The main ethical question is: "Is there a difference between killing a person and letting a person die?"

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