If I recall correctly, Jech is using as his metatheory the *class* theory $\mathsf{NBG}$. In this context, "true" is a proxy for "true in the (class-sized) structure $V$."

Specifically, the (more) formal version of the natural-language Theorem $12.7$ is the following:

> $Th(V)$ is not definable in $V$.

The definition of $Th(V)$ is taking place on the class level: it's a set of natural numbers defined by quantifying over classes. The same is true for the property "definable in $V$." So even though it looks like Jech is using a weirdly un-referring notion of "truth," it is in fact just the usual notion of truth with respect to a specific structure - that structure being $V$, and that whole facet of the argument being (annoyingly, perhaps) kept implicit.