How does the Meyr-Oerder Timing Algorithm work?
For PAM signals, the squaring creates a spectral component at $\dfrac{1}{T}$.  Consider the following trigonometric identity to understand why this is the case:

$$\cos^2\left(2\pi \dfrac{1}{2T}\right) = \dfrac{1}{2}+\dfrac{1}{2}\cos\left(2\pi \dfrac{1}{T}\right)$$

The phase of that spectral component at frequency $\dfrac{1}{T}$ is a measure of the evenness (or oddness) of the symbol relative to the reference time $t=0$ of the fourier transformed squared samples.  A phase of zero corresponds to the symbol being centered at that reference time.

The Fourier transform is used to find the phase of the $\dfrac{1}{T}$ spectral component, which is an unfiltered, scaled estimate of the symbol timing offset.