What does the amplitude in a frequency response of a signal signify?
Short answer, it depends what exactly you're looking at.

If you have a time series and compute the DFT, this will give you the concentration of energy at each discrete frequency point you have chosen. When you compute the PSD of a signal in MATLAB (using pwelch or cpsd), you'll get units of power/frequency. This describes the amount of energy or power in that specific frequency range (bin). If instead your goal is to relate the amplitudes of sinusoids in a time series directly to the values that you're reading off the peaks in the PSD plot, you need to ensure that your FFT is appropriately scaled. In the MATLAB functions cpsd() or pwelch(), the FFT is scaled such that the $\textit{total energy}$ in the signal is preserved (done by dividing by the FFT by the sampling period, $t_s$). If you want to recover the original amplitudes of a signal (e.g., $x=A_1 sin(\omega_1*pi*t)+A_2 sin(\omega_2*pi*t))$, you would want to ensure that the FFT is scaled by the duration of the signal, $T$. 

Basically, to make any accurate inference from the frequency response plot, you need to know exactly how it was computed (units). 

Some refs. that I found helpful:
What is the difference between the PSD and the Power Spectrum?