The Trolley Problem
Explanation
The Joke
The comic presents a variation on the classic trolley problem from moral philosophy. In the standard version, you must choose whether to divert a trolley to kill one person instead of five. SMBC's version escalates the scenario to increasingly absurd degrees, satirizing how philosophers endlessly generate ever-more-contrived variations of the thought experiment.
The Humor
The trolley problem is one of the most well-known thought experiments in ethics, and it has been parodied extensively. SMBC's take skewers the academic philosophy tendency to add increasingly bizarre conditions to thought experiments ("But what if the one person is your mother? But what if you know one of the five will grow up to be Hitler?"). Each new variation is supposed to test some specific moral intuition, but at a certain point the scenarios become so contrived that they stop illuminating anything useful.
The comic also implicitly comments on the gap between academic ethics (which loves these hypotheticals) and practical morality (which almost never involves trolleys on forked tracks).
Context
The trolley problem was originally formulated by philosopher Philippa Foot in 1967 and expanded by Judith Jarvis Thomson. It has since become a staple of introductory ethics courses, internet philosophy discussions, and meme culture. SMBC has returned to the trolley problem multiple times, as it's a rich target for Weinersmith's particular brand of philosophy humor.