What is principle component analysis?

There is a wonderful description at stats.stackexchange.com how science should be taught

Imagine a big family dinner, where everybody starts asking you about PCA. First you explain it to your great-grandmother; then to you grandmother; then to your mother; then to your spouse; finally, to your daughter (who is a mathematician). Each time the next person is less of a layman. Here is how the conversation might go

This science not by some older science journalists or some younger science slammers but a real expert.