We all know that the wave vector of a propagating plane electromagnetic wave indicates the direction of propagation. What does it mean by the "in-plane" wave vector of that plane wave?
Depends on the relation of the wave to a medium, interface or scattering geometry.
in-plane almost certainly does not refer to the plane of constant phase of the wave, but to a plane of the rest of the problem.
For example, if your wave is propagating inside a hexagonal crystal, in-plane will refer to the component parallel to the a-b planes of the crsytal (or perpendicular to the c-axis)