You measure the BP of a group of people and then, without treatment and under similar conditions, you measure them again. Perhaps unexpectedly, you find that on average, those with the highest BPs the first time tend to have reduced BP levels the second time and those with the lowest BP the first time tend to have slightly increased BP the second time on average. In other words, on average the BPs after tend to be close to the mean BP than the BPs before. But note, this has nothing to do with physiology - it is purely a statistical artifact. (Perhaps even more unexpectedly, those with the highest BPs the second time tended to have BPs a little lower the first time, and vice versa.)

If you plot a graph of BP after up, and BP before across (or vice versa) you get the expected upward trend, and if conditions are the same you would expect the slope of the best fit line to be 1. However, it will be less than that. In this situation the slope is a measure of the correlation between the before and the after BPs and would be an estimate of the effect of the regression to the mean.