That the phase speed can have a dependence on the wavelength/frequency of the wave. For instance, a whistler mode wave can have a cubic dispersion relation at low frequencies. In this limit, the higher(smaller) frequencies(wavelengths) propagate faster than the converse. It results in a sort of "spreading out" of the wave modes. This if often seen upstream of collisionless magnetized shocks in space.
You can also graph $\omega$ vs. $\kappa$ and show that the slope of the line at any given ($\omega$, $\kappa$) point corresponds to the group velocity and the ratio $\omega$/$\kappa$ corresponds to the phase velocity.
For instance, see the image below, modified from an figure in Krauss-Varban and Omidi, :
The $\omega$ vs. $\kappa$ diagram has been Doppler-shifted into a shock rest frame for this specific example, but it should illustrate my point. Where the frequency goes to zero on this plot corresponds to a phase-standing mode (i.e., zero phase velocity) in this frame of reference. In another frame, the same mode would have a finite phase velocity. Where the slope of the blue line goes to zero, the wave's group velocity is zero (or group standing).
Does that help?
Krauss-Varban, D., and N. Omidi "Structure of medium Mach number quasi-parallel shocks: Upstream and downstream waves," Journal of Geophysical Research 11, pp. 17,715--17,731, 1991.