The speed of a sound wave (or a seismic wave which is a type of sound wave) depends on the density of the stuff it travels through and also on the" squeezability" of the stuff it travels through. Each substance has its own unique set of properties, hence if we measure the sound speed for the real earth we can compare with the sound speed of different rocks and then say something approximately correct about what the nature of the Earth is like at depths which we cannot directly observe.

Sound travels through different materials at different speeds, which means that sound waves bend as they travel across transitions in materials, just as light waves do (this is why you can see surfaces of water, glass, etc., because light waves also travel at different speeds through different materials). By measuring the rates at which sound speeds differ, we can figure out what the materials they're traveling through are.