Maxwell's equations in differential form state that $\vec\nabla\cdot\vec E=\rho$ so that the divergence of the electric field corresponds to sources and sinks of the electric field, i.e. to charges. You will undoubtedly give for your students, either in class, or for out-of-class reading, a short derivation of the differential form of Maxwell's equation, using the divergence theorem. But this derivation alone, or even an emphatic statement from you about the physical meaning of the law is not sufficient to allow students to understand and internalize this result. They will need some chances to engage with the implications. Here are some suggestions:

1. Check if Colorado has Peer Instruction questions about this.
2. Show them several different electric field configurations and ask the students to figure out what charge distribution they come from. ( We should provide several plots).
3. Ask your students to draw a vector field that corresponds to $\vec\nabla\cdot\vec E=2$ inside an infinite cylinder and $\vec\nabla\cdot\vec E=0$ outside the cylinder. There are several different answers to this question. A class discussion should help the students to realize that they also need $\vec\nabla\times\vec E=0$, the other Maxwell equation, to distinguish between these possibilities. Don't forget to ask you students to describe which charge distribution this corresponds to. Alternatively, ask the question the other way around. Give them the charge distribution and ask them to draw the field. Do they automatically choose a field with cylindrical symmetry? If so, why? Ask if this is the only possibility.
4. This is an excellent opportunity to talk about the difference between discrete point charges and volume charge densities. What is the volume charge density for a finite discrete point charge $q$? Your students will need to know something about delta functions to answer this question.