The cepstrum is commonly referred to as a "spectrum of a spectrum." By performing $\mathbf{X}=\mathbf{W}\mathbf{x}$, you are calculating the complex result of the discrete Fourier transform of your input $\mathbf{x}$. Taking the squared absolute value of $\mathbf{X}$ renders the energy spectral density, which simply expresses the energy of $\mathbf{x}$ at each frequency of the spectrum and disregards any information about phase.
$$ E_{\mathbf{x}} =|\mathbf{X}|^2$$
Recalling the logarithmic property,
$$c \log x=\log x^c,$$
it is clear that $\mathbf{X}_{dB}$ is the decibel representation of the energy spectral density:
$$\mathbf{X}_{dB}=20 \log_{10}|\mathbf{X}|=10 \log_{10}|\mathbf{X}|^2=10 \log_{10}E_{\mathbf{x}}.$$
Note that $\mathbf{X}_{dB}$ is a purely real quantity. Finally, the cepstrum, $\mathbf{c}$, is found by taking the discrete Fourier transform of $\mathbf{X}_{dB}$, again exposing a complex spectrum that now describes the periodic components of the energy spectral density. A "peak" in the cepstrum at anywhere other than DC (i.e. $k\ne0$) means that the energy spectral density has periodic components (e.g. harmonics). The frequency spacing of these harmonics in $E_\mathbf{x}$ would correspond to the location of the peak in the cepstrum, also known as quefrency. The value at DC, $c[0]$, would describe the broadband energy of $\mathbf{x}$, or how much the entire spectrum is positively offset for all frequencies.
The reason for the $\log_{10}$ scaling in this is to reduce undesired artifacts from showing up in the cepstrum, which can be observed if you take the Fourier transform of a periodic pulse train.
