IIRC, Erwin Schrödinger created the thought experiment as a critique of the popular theories surrounding quantum mechanics. (Wikipedia calls it Copenhagen interpretation, but I'm not a physicist so I'm not gonna pretend I know what that means.)
Again, I'm in no way qualified to explain this, but from what I've been able to understand, subatomic particles are constantly moving. Because they're constantly moving, it's not possible (by current means) to detect where any particle is at any given time. So, the best way scientists found to work with this constant movement was by assuming the particle was in more than one place at the same time.
Erwin Schrödinger, in a discussion with Albert Einstein, allegedly gave this analogy to describe the issue with this idea, that something simply can't be in multiple states at the same time. Ironically, this analogy became one of the most popular ways of explaining quantum physics.
Someone tell me I'm stupid if this is wrong or doesn't make sense.