Among that stuff was that if you take people from one end of a distribution and see where they are on another distribution, the second average will always be closer to the mean than the first. My friend, Julie, got a good score on a promotional test, but decided it wouldn't hurt to take the test again. To her surprise her score went down one point. It was still a high score, but the one point drop was worth complaining about. The regression effect.
People just trade errors of measurement.
People who had scores above the mean on the original test more likely had positive errors of measurement. Of those who had positive errors, some will have a larger positive error on another test, some a smaller positive error, but some people's errors will change from positive to negative. Their average error of measurement will be zero. Since the average error is lower, their average observed score is lower. Analogously, those who originally had negative errors will on the average have less negative errors.