A figure 8 or grackle nosband is used to prevent a horse from crossing its jaw over and avoiding contact or the bit, this type of noseband only works when applied correctly so always ask for help from a trainer or knowledgeable person the first time you use one to make sure you have it fitted correctly.
From what I wasn't taught the figure eight was designed for certain pressure points on the horses nose. It helps even out the pressure in comparison to a flash. If you have a horse that constantly raises his head before the jump or constantly opens his mouth this bridle prevents the horse from pulling against you as much. Of course everyone has different views on the purpose behind the setup!