The footbox does four main things.
1. Allows you to lie a bit further on the diagonal to get a flat lay that is difficult to match by other gathered-end hammocks.
2. Allows you to also slide a bit further towards the foot end. For me, this frees up some head space and makes the reciprocal "head box" unnecessary, although that's a really interesting idea. YMMV, especially for taller people.
3. Prevents the heels and calves from digging into the hammock fabric when properly adjusted.
4. Provides a wall to prevents feet from slipping out of the hammock. I think the comments about the bug netting simply refer to the fact that Brandon didn't run the netting all the way down to the feet area, which would likely have been a less comfortable and weaker design. That is a bonus though and certainly not the main goal of the footbox.
"The Road goes ever on and on,
Down from the door where it began.
Now far ahead the Road has gone,
And I must follow, if I can.
Pursuing it with eager feet
Until it joins some larger way
Where many paths and errands meet.
And whither then? I cannot say."
~Bilbo Baggins - LotR