A compound word like breakdown almost always has roots based in the two words from which it was made, but over time words gain additional meanings and can change quite dramatically. The roots of this one are still fairly straightforward though, and we still use the words break down as the verb form of the noun breakdown.
Breakdown once meant a collapse, as in a building breaking apart and falling down. It later took on the meaning of intentionally dismantling an object. Boy Scouts might break down their tents as part of striking camp. Taking something apart often involves categorizing the parts. We still say that a cook breaks down a chicken or a fish when he or she cuts it into parts, for instance.
In much the same way, a figurative breakdown, as in your quotation, is an analysis that splits an object into its parts.