Bicycle seat height
 

In these formulas, they make reference to the "bottom bracket". Just where is the bottom bracket?? Bottom bracket of what?

The center of the circle that your pedals make when you turn them.

The term "bottom bracket" refers to the spindle to which your cranks are mounted, the whole bearing assembly and the shell of the bicycle frame that surrounds the assembly depending on the context. When the topic is bike fit, as it is here, it refers to the centerline of the bottom bracket spindle. You can measure (from say your seat) to the center of the bolt or cap on the crank arm on cranks where the spindle does not pass through.

Ben

And that center axis is the bottom end of the measured seat tube length, commonly called the 'bike frame size'.