P, S and L waves refer to Primary, Secondary and Longitudinal waves. L is also the first letter in Love waves. See explanation.

Waves are propagated through a medium that is a solid or a fluid ( liquid or gas ). So, there is velocity in this propagation. If the propagation is like or unlike, in the direction of the velocity, the waves are called longitudinal. Otherwise, they are called transverse waves.. Primary waves are bundle of longitudinal waves that travel through both solid and fluid mediums. Secondary waves are bundle of transverse waves that cannot easily travel in a solid medium. The propagation depends on the resistance (shear force ) offered by the medium. Naturally, the resistance is more from solids. Of course, this resistance indeed affects the propagation of primary waves. Waves involve movement of ground, perpendicular to the direction of the velocity of propagation. When the amplitude of the motion is parallel to the surface, the wave is called a Love wave.