The top rein acts just like a snaffle, by putting direct pressure backwards on the top of the tongue and bars. With a jointed mouthpiece, the collapse of the bit will also apply pressure to the outside of the lips and bars
The bottom, or ‘curb’ rein gives the rider leverage, so he can rotate the mouthpiece downwards and engage the curb chain, thereby dividing the rein pressure between the mouthpiece and the curb.
The widespread notion that curb pressure is severe or unkind is not at all true: For a start, the curb area is a lot less sensitive than the horse’s tongue! Curb pressure helps to encourage the horse to flex at the poll. (The higher up the back of the jaw this pressure is applied, the more it will prompt the horse to flex from the base of the neck, helping him to lift his withers and come into a correct outline.)
The curb chain restricts the extent to which the mouthpiece can rotate down onto the tongue; and it also shares some of the rein pressure, so it is not all on the mouth.
Curb rein pressure will also apply a small amount of pressure to the poll, but this releases endorphins, so it is normally a positive influence.
Use of Pelham “roundings”, which convert the bit to use a single rein, does not properly combine the two actions, it basically turns the bit into a snaffle, minimising the downwards rotation of the mouthpiece and merely loosening the curb chain. The rider may just as well ride with the top rein only.