ELI5: Explain Like I'm 5

Uniqueness theorem for Poisson's equation

The Uniqueness Theorem for Poisson's equation says that if you have a situation where you have two functions that both satisfy Poisson's equation (which is a partial differential equation used to describe physical situations like electrostatic potential), then those two functions must be the same. In other words, if something is described by Poisson's equation, then it can only be described one way even if there are different ways that it looks like.