The following paragraph appears in Analytic Number Theory (Iwaniec, Kowalski):

The Siegel-Walfisz theorem asserts that:

$\displaystyle \hspace{5cm} \psi(x;q,a) = \frac{x}{\phi(q)} + O(x(\log x)^{-A})$

for any $q\geq 1, (a,q)=1, x\geq 2$ and $A\geq 0$. **Notice that this estimate is non-trivial only if $q \ll (\log x)^A$**.

The last sentence is somewhat clear to me intuitively, and ought to answer my question. But I am not quite sure what Vinogradov's '$\ll$' notation is taken to mean in this context, as $q$ is not even a function of $x$. Can anyone clarify this?