How can I explain the Coulomb's law equation?
There is no such explanation of Coulomb's law.
Electric force (more strictly, electromagnetic force) is a fundamental interaction of mother nature.
The electrical the force depends on the product of the magnitude of the two charges and is inversely proportional to the square of the distance between them. It acts along the line joining the two charges. (We assume that they are point charges).
The Coulomb force also satisfies the superposition principle.
It is how nature made it.
Now, if you ask, why does unlike charges attract and like charges repel, it is not possible to answer such questions. In fact, such questions belong to the domain of philosophy and metaphysics.
We can however, measure the force.