With a plane wave, I always took the direction of the
wavevector, k, as the direction of propogation (magnitude
proportional to the inverse wavelength). Alternatively, it could
represent the momentum (minus a factor ?) of a particle.
However inside a crystal, the electron wavevector and the
electron velocity are not necessarily in the same direction. I'm
thinking here of a 2D material with a cylindrical Fermi surface
where the momentum may have a z component, but the Fermi velocity
does...