$\epsilon_0$ is epsilon naught, or permittivity of free space.
Let me preface this by saying that I've just started to learn about electromagnetism. When I first saw Coulomb's law, I was incredibly confused to why the proportionality constant was exactly $1/4\epsilon_0$. Then I saw that this was derived from Gauss's law. In Gauss's law though, the constant of proportionality is $1/\epsilon_0$. Then I wondered how that is true? I researched more and find that most people derive Gauss's law from Coulomb's law. So it seem's to be more like circular reasoning?
This might be similar to this question: What was discovered first - The Coulomb constant or Gauss law?
But I find the answer here not satisfactory in that it never explains why the constant of proportionality is $1/\epsilon_0$. I kind of get that Gauss's law is a mathematical theorem and that it comes from something called the Divergence theorem that is then applied to electrostatics. I don't understand the math because it is not at my level but I can understand why the general form of the equation is like that. What I don't get is why that formula has $\epsilon_0$ as the proportionality constant. Where did it come from?
I hope my question makes sense. To summarize: What I want to know is, why is $\epsilon_0$ in these equations and how?