What does this equation mean?

This is an exact solution describing flat Minkowski spacetime in non-inertial coordinates, not a weak-field approximation. A clock held static at height Z has d$\tau$ = U(Z)\,dt exactly, so two such clocks compare frequencies as $\nu_2$/$\nu_1$ = U($Z_1$)/U($Z_2$) to all orders — the same exact redshift formula an accelerating rocket produces for light climbing or falling inside it. The node potential is $\phi(Z)$ = $\ln$ U(Z) = $\ln(1 + gZ/c^2)$ , and its first derivative at Z=0 is $\phi$' = g/$c^2$ : a nonzero, entirely real, measurable slope. A network of clocks bolted to this elevator’s walls would report exactly the nonzero edge data a network in a genuine gravitational field reports at the same order. If a nonzero slope alone were curvature, this elevator would be curved. It is not; by construction its spacetime is exactly flat, and the geodesic deviation between any two nearby free-falling test particles inside it is exactly zero at every instant, because flatness is a property of the manifold and does not care what coordinates — accelerated, rotating, or otherwise — a particular family of observers happens to use.