Vacuum expectation vs ensemble average

On p.169 of Dodelson’s Modern Cosmology, the following is stated:

"We can compute the quantum fluctuations of the operator $hat{x}$ in the ground state $|0rangle$:
$$ big langle |hat{x}|^2 big rangle = langle 0 | hat{x}^{dagger} hat{x} | 0 rangle.$$
We will later identify $hat{x}$ with the field $phi$ […]. In later chapters we will use the same notation to denote ensemble averages of observables, that is, the value of an observable if it were measured over an infinite volume. These two are not same. We can, however, equate them if our universe is only a small part of a larger patch of spacetime that underwent inflation."

What does this statement mean? Can someone elaborate on why this identification is justified under the given assumption?

Many thanks in advance.