Welch's Power Spectral Density - Time-Averaging Explanation
Periodogram averaging means that the squared DFTs of consecutive frames are averaged (per frequency bin). If $k$ denotes the frequency index and $l$ denotes the frame index, the averaged periodogram is computed as

$$\overline{P}[k]=\frac{1}{L}\sum_{l=0}^{L-1}P[k,l]\tag{1}$$

where $P[k,l]$ is the $k^{th}$ element of the squared magnitude of the DFT of the frame with index $l$. In (1) the averaging is done over $L$ frames. This is only useful if the signal can be assumed to be stationary during these $L$ time frames.