Usually, something like this is used to keep various parts of the bridle from slipping, getting hung up on another strap or the bit or otherwise flapping around so it stays in the proper place and still. Lots of movement created when jumping the bigger stuff.
It could also be part of a gag arrangement or to keep the bit still and in exactly the place it needs to be.
When opportunity knocks it's wearing overalls and looks like work.
I can't see enough of the bit to tell, but Mikmar makes (or used to make) a combination bit that includes a nose rope. If that is indeed a Mikmar bit, the short answer to your question is that when you pull back on the reins some of the pressure is distributed over the horse's nose.
It looks like an older Mikmar combination bit model, before they added the leather sheath to it. I used the same bit on my horse. The string helped refocus him much better than more conventional bits since he tended to brace, invert, flip me off, and then run at the jump. While we used a french link snaffle at home, the Mikmar was an awesome bit for this horse to get things done in when it counted.