The Belly is where most of the weight of the fly line is stored and is the section between the front taper and the rear taper. The belly is usually the same diameter for its entire length but some lines have taper changes within the belly section.
Some lines offer different shaped belly sections like the Wulff lines are the shape of a triangle or the Airflow Ridge line that has tiny ridges. Both of these lines are creating less surface resistance from the line gliding through the guides of the rod. This in return will create more efficient casting.
When casting you need to have the correct amount of weight of line outside the rod tip to load the rod enough to make the cast you would like to make. In most situations having the entire belly of the line outside your tip will load and store enough energy in the rod to make most fishing casts.
I will break down this is future casting post so stay tuned.