Complex sentence: In isotropic and homogeneous solids, the polarization of a P-wave is always longitudinal; thus, the particles in the solid have vibrations along or parallel to the travel direction of the wave energy.
Split into simpler sentences: In isotropic and homogeneous solids, the polarization of P-waves is always longitudinal. This means that the particles in the body have vibrations along or parallel to the direction of travel of the wave energy.