The wave motion is disturbance travelling through a medium with the help of motion of particles of the medium. The particles of the medium vibrate and assist the disturbance in continuing.
When the motion of particles of the medium vibrate in the direction of the motion of disturbance, such a wave is called as longitudinal wave motion.
The best example foe this would be Sound waves.
Thus, Longitudinal wave motion is when the particles of the medium vibrate in the same direction of motion of the wave.