The Classic Scenario
In the trolley problem, a runaway trolley is heading down a track toward five people who will be killed if nothing is done. You are standing next to a switch that can divert the trolley to a different track, where it will kill one person instead. The question asks: should you pull the switch? This simple scenario creates a difficult moral choice between action and inaction.
The Transplant Variation
Another version presents a different situation: a doctor has five patients who will die without organ transplants. A healthy person walks into the hospital, and the doctor could kill this one healthy person and use their organs to save the five patients. Most people say this is wrong, even though the math is the same as the trolley problem. This variation shows that people's moral intuitions change based on how directly you cause harm.
What It Reveals About Ethics
The trolley problem exposes differences between two major ethical approaches. Consequentialism focuses on outcomes and says saving five lives is better than saving one. Deontological ethics focuses on duties and rules and says directly killing an innocent person is always wrong, even to save others. Most people's gut reactions follow deontological thinking, but their reasoning often involves consequentialist ideas.
Action Versus Inaction
A key insight from the trolley problem is the difference between actively causing harm and allowing harm to happen. Most people feel more guilty pulling a switch that kills one person than they do failing to pull a switch that would save five. This reveals that people consider the action itself, not just the final outcome, when making moral judgments.
Real-World Applications
The trolley problem helps philosophers think about real-world ethical dilemmas in medicine, law, and public policy. For example, it relates to questions about whether doctors should ration limited medical resources, whether self-driving cars should be programmed to minimize deaths, and whether governments can harm some citizens to protect others during emergencies. 
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