What is permittivity in free space? From Coulomb's law, we know that $\epsilon_0$ means permittivity in free space. It's unit is $\rm C^2 N^{-1} M^{-2}$ ( coulomb squared per Newton per square meter).
But what does it mean physically?
For example, 1 Pa pressure means 1 Newton force applied perpendicularly on 1 square meter area. In a similar way, can anyone please describe $\epsilon_0$? 
 A: It comes from Coulomb's electrostatic law:
$$F = \frac{1}{4\,\pi\,\epsilon_0}\,\frac{q_1\,q_2}{r^2}$$
for the force between two charges $q_1,\,q_2$ spaced by a distance $r$.
So then $(4\,\pi\,\epsilon_0)^{-1}$ is simply the force between two charges of one coulomb each spaced at a distance of 1 meter. The ${\rm C^2}$ in the unit definition means that if either of the charges are multiplied by a factor, the force scales in proportion: if both are multiplied by the same factor, the force thus scales by that factor squared (look at the right hand side of the equation). Likewise, the ${\rm m^{-2}}$ in the definition means that the force scales inversely with the squared distance (likewise a pressure has $m^{-2}$ in its units because if you multiply the sidelengths of the square a force acts on, you diminish the force by that factor squared). So if you re-arranged the equation as $F r^2\,q_1^{-1}\,q_2^{-1} = (4\,\pi\,\epsilon_0)^{-1}$ both sides need to have the same units, hence the units you see.
As for why we call the scaling constant $(4\,\pi\,\epsilon_0)^{-1}$ rather than some simple constant $G$, well that's simply a matter of taste. It makes another form of the law (Gauss's law) easier to write. But a perfectly well defined system of physical constants could have been defined with the constant defined the "simpler" way. In fact, in Newton's universal gravitation law (which is also an inverse square law), that's the path we fickle physicists have historically chosen to take!
A: Maybe a slight easier to follow answer, based on the Quora Website 
The permittivity of free space is a  number which allows us to describe how easily (or how difficult) it is for electric lines of force to pass through air, water or any other medium. 
It's called permittivity because of how much a given substance "permits" electric, (or magnetic in the case of magnetism ) field lines to pass through them.

Imagine a positive charge placed in free space , you know that all its lines of forces are directed outward with equal distances between them , but if we place a material through which electric field lines pass more easily than free space , than its permittivity is more compared to free space and hence more electric lines of force will pass through it , and more importantly it varies with variation of medium.

So for some substances, electric field lines will pass them through easily, and for other, depending on their composition, they won't.  
