What is meant by "correlation" when referring to spectral coherence
The coherence function, as used in signal processing, measures the normalized correlation between to power spectra:

$$
C_{xy}(f) = \frac{|G_{xy}(f)|^2}{G_{xx}(f) G_{yy}(f)}
$$

where $G_{xx}$ is the power spectral density (PSD) of the signal $x(t)$, $G_{yy}$ is the PSD of $y(t)$, and $G_{xy}$ is the cross-spectral density (CSD) of $x(t)$ and $y(t)$.

The CSD is computed as the Fourier transform of the cross correlation of $x$ and $y$:

$$
R_{xy}(\tau) = \operatorname{E} \left[ x(t) y(t + \tau) \right]
$$
$$
G_{xy}(f) = \mathcal{F} \left[ R_{xy} (\tau) \right]
$$

You can think of the CSD as measuring "hidden periodicities" in the cross correlation, just like the PSD measures periodicities in the autocorrelation. (This is where the name for the "periodogram" PSD estimator comes from.)

Incidentally, if the cross-correlation has harmonic content at some frequency $f$, you can think of the signals being correlated at that frequency.