You might have noticed that a lot of jumpers seem to use the figure-eight noseband as opposed to a regular cavesson or a regular cavesson with a flash.
There are several reasons why a rider might choose this type of noseband over another. Sometimes it is used simply because it is popular and riders like the look of it. More often, it serves a genuine purpose that a regular cavesson does not provide.
The figure-eight noseband is similar to the flash noseband in that both keep the horse's mouth from opening too wide. This can be very handy on course when your horse gets strong and you need to keep him from going too far in evading you. The figure-eight noseband goes one step further and also keeps the horse from crossing its jaw because the top of the noseband is fastened much higher up on the face.
The figure-eight has an advantage over the flash because it allows the horse to breathe more freely. A tightly fastened flash noseband can often restrict breathing if the horse flares its nostrils while working hard. Because the figure-eight crosses much higher than a flash would attach, it leaves room for the nostrils to expand. One downside of the figure-eight is that if you plan on using a standing martingale (allowed in some low jumper classes), you will need a regular cavesson to attach it to.
From personal experience, I have found several horses to actually prefer the figure-eight over a flash noseband or even just a regular cavesson. I can only imagine that this is because the figure-eight doesn't really squeeze around any teeth since the higher strap passes over a padded section of the jaw and the lower strap passes over the interdental space. A regular cavesson, on the other hand, passes directly over the premolars.