What does this equation mean?

It is worth being precise about what kind of object each chart in this pairing actually is, because the two are not interchangeable answers to the same experiment. $X^\mu(u,\Sigma)$ , built from a classical or semiclassical stress-energy distribution, is a number: a spacetime point associated with one physical configuration. $\mathbf X_{\mathrm{NW}}$ is an operator on a Hilbert space, and what a quantum experiment actually reports is not $\mathbf X_{\mathrm{NW}}$ itself but expectation values and, eventually, click statistics built from it. The two charts answer “where is it” for two different kinds of description of the same underlying physics, classical field and quantum state, and the atlas has to keep that distinction visible rather than silently identifying an operator with a number.