Compare S (secondary) waves and P (primary) waves. Why do they travel at different speeds?

S waves

These are shear waves. The motion of the medium is perpendicular to direction of propagation of the wave. They can propagate only through solids and not through gases or liquids. S waves are larger. They travel with less speed.

P waves

These are compression waves. These waves produces a force along the direction of propagation. They can propagate through solids, gases and liquids. P waves are smaller than s waves. They travel with 60% greater speed than S waves.

P-waves travel 60% faster than S-waves on average because the interior part of the Earth does not react the same way as the s wave and P wave.