I would take it to mean that, for the Electric field $\overrightarrow{E}$.
$$\overrightarrow{\nabla}\cdot\overrightarrow{E}=0$$
Everywhere within your charge-free region (lets call it M). Intuitively you can think of a point charge as a place where all of the electric field lines begin or end. picture the field as several arrows, they will point toward or away from the charge, this is what the divergence in the above equation measures.
You could also consider (applying Gauss's Law to the above) to be:
$$\int_{\partial M}\overrightarrow{E}\cdot d\overrightarrow{a}=0$$ where $\partial M$ denotes the boundary of the charge free region. Though this is less helpful as it really means the total charge is zero in M (so you could have charges here so long as they sum to zero).