Full Cheek or Fulmer Snaffle Bit
For horses that need help from the bit in turning, the full cheek is the most extreme type of corrective cheek piece that can commonly be found on a snaffle. With a small ring fixed to the mouthpiece on a swivel joint, and two arms extending above and below the mouthpiece, the main purpose of this bit is to exert lateral pressure on the horse’s mouth. When one side of the bit is pulled, as in turning, the opposite side presses against a broad section of the lips and cheeks. This can be particularly useful with horses that are having difficulty learning to respond properly to direct rein pressure, and can sometimes help correct horses who tip their heads trying to evade direct rein pressure. With horses who may evade direct rein pressure by opening their mouths or otherwise making it possible for the bit to be pulled through the mouth completely, a full-cheek snaffle can prevent this problem. A full cheek snaffle is also useful when rein aids may be the main way to communicate lateral cues, such as when driving, riding side saddle, or in para-equestrian.
Information from thebitguide.com