The diamond principle in theorem 13.21 of Jech : There exists Z = $\langle S_\alpha : \alpha < \omega_1\rangle$ with $S_\alpha\subset \alpha$, such that for every X $\subset \omega_1$, the set Y=$\{\alpha < \omega_1 : X \cap \alpha = S_\alpha\}$ is a stationary subset of $\omega_1$.
If X is a single ordinal $\beta$ (which could be the empty set $\phi$ ) , then Y would have a maximum $\alpha$ with $\beta \cap\alpha$ = $S_\alpha$ if the $S_\alpha$ are "increasing in size as $\alpha$ increases", which would mean Y isn't stationary. However if Z includes a cofinal sequence of "special" $S_\alpha$ all of which are = $\beta$ (i.e. $\langle$$\alpha$ : $S_\alpha$=$\beta$$\rangle$ is cofinal in $\omega_1$) then this would allow Y to become big enough to have a chance of being stationary, as the diamond principle applies to all subsets X of $\omega_1$ ?
Is this the essence of the diamond principle - is it all about how cofinal sequences of identical sets (for a given X) can be interleaved together to allow a large stationary set to be made, by requiring that it applies to all $X\subset \omega_1$? With this interpretation it looks quite hard to do in general without limiting what the X can be - as there are so many X in general (though in the constructible universe the number of X is limited so the intuition would be that it "looks" achievable there, which is the case by Theorem 13.21).
Please see all of the comments, thanks.
Note that for unbounded X, X $\cap \alpha$ = $S_\alpha$ picks out those $S_\alpha$ that are initial segments of X, so if X is unbounded there will be an unbounded sequence of $S_\alpha$ that increasingly approximate X via its initial segments. So as the diamond principle applies to all X which are subsets of $\omega_1$, the sequence Z will contain limiting approximations to all subsets of $\omega_1$.