Pelham bit
The pelham combines snaffle and curb action in one mouthpiece with two pairs of reins.
What is it for?
It gives access to both direct pressure and leverage with a single mouthpiece.
More about this item
The pelham is designed to mimic a double bridle with one mouthpiece. The top rein acts as a snaffle, the lower one with the shanks as a curb. Two rings are sometimes joined by short straps (roundings) so a rider can use a single pair of reins.
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Sources: Wikipedia · British Horse Society. Descriptive only; not care or training advice.