According to this post that Alexei Beltyukov shared, the standing broad jump is an exercise at the combine just like the vertical jump and the 40 yard dash. It is a number that scouts write down on paper. That is it.
Byron Jones jumped 12 feet 3 inches from a dead standstill. Go watch the video for yourself if you want to see someone who is such a sick athlete that he probably does not even realize he could be a world class track and field athlete.
Dear Byron, I have no problem with you wanting to play in the NFL. We all want to play in the NFL, and I hope you make it. I really do. However, if you do not make it to the NFL, please go into track and field. For all that is holy, find some events you can do. I would be willing to bet you could slim down and do the long jump. I am also willing to bet your could do discus, javelin, shot put and hammer throw. Please do it because you could be a gold medalist many times over with skills like that.