Suppose you are a surgeon with five patients in critical condition. One will die very soon if she does not get a new lung, one will die without a new kidney, another without a new heart, another without a new liver, and the last without a new stomach. But you also have, in your clinic right now, John Doe, a perfectly healthy young man who has come in to fix the photocopier. And you just happen to know (never mind how) that John Doe is a perfect donor for each of your desperately needy patients. So you kill him and use his organs to save the lives of your patients. You have saved five lives at the cost of one.
Now, most would agree that what you did was morally wrong. It is not morally permissible (or is it?) to treat people in the way you treated John Doe.
But now suppose that you are the driver of a runaway railway engine. You have little control of the engine: you cannot stop it or even slow it down (and it is going very, very fast). But you do have a little bit of control. If you come to a junction, for example, you can cause the engine to take the right fork or the left fork. Now, suppose you see a junction coming up fast, and suppose that, on the right fork, there are five workmen on the line, whereas on the left fork, there is only one workman on the line. You cannot warn them of your approach, and it is highly unlikely that they will see or hear you coming (their backs are turned, and they all have on their Sony Walkmans). Then you should take the left fork, no? You should take the left fork, because that way you will save five lives at the cost of one.
But wait a minute! How can it be morally required that you save five lives at the cost of one in the runaway train example, but morally wrong to save five lives at the cost of one in the surgeon example? Are you intrigued? Worried? Would you like to be able to think clearly, creatively, and effectively about this sort of question? If you would, then you should think about studying philosophy. Welcome to philosophy at Hampden-Sydney College!