Meaning of the inverse of a differential operator

Meaning of the inverse of a differential operator

Consider the Poisson's equation $$\nabla^2\phi(\textbf{x})=-\rho(\textbf{x})/\epsilon_0.$$ What is the meaning of the inverse operator in the following $$\phi(\textbf{x})=-\frac{1}{\nabla^2}\frac{\rho(...