Answer
The probability amplitude is what "waves".
Work Step by Step
The solution to Schrodinger's equation is a matter wave, the wave function $\psi$. The physical interpretation of $\psi$ is as a probability amplitude.
The particle associated with the matter wave is more likely to be found where $\psi$ has a large amplitude, i.e., where it is large. The particle is less likely to be found where $\psi$ has a small amplitude, i.e., where it is small.
The probability density function, $|\psi|^{2}$, is the square of the probability amplitude.
This is discussed on page 610.