I'm not confident that there is a way to explain this to the layman without the nitty-gritty of all the math and hardware and manufacturer choices in processing raw data. A simple analogy that could work would be audible hiss in an audio tape recorder, where you recorded with levels that were too high or too low, and you tried to fix them after they were mixed with the hiss. If the mic levels were too high, you might reduce the gain as you play back the recording, and you will make the hiss a little quieter. If the mic levels were too low, you might boost the levels as you play back the recording, boosting the level of the hiss. The component of noise called "Post-gain read noise" is analogous to hiss.
Regarding the raw data itself, these deviations away from a simple consistent PDR trend are the results of pushing and pulling select ISOs with math or pushing with a late-stage amplifier at the ADC. Many cameras do not have unique analog gain for every 1/3-stop ISO setting, and are forced into inconsistency. For a camera like the Canon 5D3, we get something like this:
Post-gain
ISO Analog gain Headroom read noise DR
50 100 -1 stop -1 stop
100 100
125 100 +1/3 stop -1/3 stop
160 200 -1/3 stop -1/3 stop
200 200
250 200 +1/3 stop -1/3 stop
320 400 -1/3 stop -1/3 stop
This inconsistency has no effect on photon noise or the pre-gain read noise, but it does directly drive the post-gain read noise up and down along with the pushes and the pulls, and can lose headroom, too, relative to metered middle grey for the ISO setting. At high ISOs, the post-gain read noise is very small compared to the photon noise and the pre-gain read noise, so pushing and pulling change the total noise level variation much less, but at low ISOs, post-gain read noise is the dominant noise in deep shadows. Since DR is limited on the bottom end by noise, pushes increase noise without increasing headroom (because of bit-depth clipping). Pulls will lower the post-gain noise, but also pull down the clipping point, too, so the person's 5D3 is probably losing 1/3 stop of DR at ISOs 125 and 250, but isn't gaining any at ISOs 160 and 320. This all assumes that the manufacturer is not using a clipping point below that of the original raw data readout. Bill's PDR does not look at exact clipping levels, so expect up to 1/3 stop of missing PDR with cameras that pull some of their ISOs by 1/3 stop. He just assumes that 16383 is the highest raw value used, in a 14-bit raw, which is sometimes not the case, such as when the ISOs are pulled.
So, for what "PDR" is intended to be, which is DR by Bill's standard, the PDR boosts at ISOs 160 and 320 are not really there. However, if you use PDR for what it was not intended, a noise metric, then it just happens to be accidentally significant, and images will have deep shadow noise that is lower at ISOs 160 and 320 on a camera like the 5D3.