What does it mean to partition variation? What's special about the variance — the square of the
standard deviation — as a way to measure variation?

Partitioning variation is a method of assessing variations between groups within a dataset. The variance is special because it is a measure of how far a set of numbers is spread out from their average or mean and can be used to measure how different the data points in a set are from one another. It is also the square of the standard deviation which is useful professional because it allows for more accurate and clearer interpretation of the data.