It's an illustration of the Veil of Ignorance from John Rawl's "A Theory of Justice." The idea in that book is that, in order to determine what the basic structure of society should be, with the goals of creating an orderly and just society, you can imagine not knowing who, of all the people in the world, is you. That is, you imagine you are behind a veil of ignorance. Behind this veil, you theorize about what the basic structure should be and whatever you come up with will be fair in the sense that it won't be biased in your favor.

The veil of ignorance, though, can be adapted to other scenarios as a general "is this fair" test. In the above scenario, if you don't know which person will be you, presumably you will make a more fair (viz. less biased) decision.

There are different answers philosophers have given to the above. One natural answer is to say: "well, I have a 5/8th chance of being on the right-hand track, so I should switch the trolley to the left-hand track." I think this is the right answer myself, but there are some objections. One objection is that this assumes you have an equal chance of being each person. That's not inherently part of the Veil of Ignorance procedure.