The snaffle is one of the families of bits, and A jointed snaffle is just what it says - two pieces of metal joined by a 'joint' in the middle, which acts on the lips and corners of the mouth, the tongue, and the bars of the mouth. It has a 'nutcracker' action which some horses find objectionable, but as with all bits, it is only as kind as the hands of the rider.
A gentler option, which still works in the same way minus the nutcracker action, is a french link, or double-jointed snaffle. It has a rounded central plate which lies flat across the tongue. The action of the bit works in the same way as the single-jointed snaffle, but minus the painful nutcracker option. It's a useful bit for horse's with big tongues or narrow mouths, but personally I find horses prefer the french link to a single joint. Don't confuse a french link with a Dr Bristol, which has a squared-off plate in the middle, which is set on at an angle to press into the tongue!
Personally, I would choose a french link over a jointed snaffle any day, as the french link is just about the mildest bit you can buy. Having said that, any bit is only as gentle and effective as the rider's hands - I'd rather see a horse go sweetly in a double bridle with a rider with soft, light hands (like my two horses do) than to see someone sawing away on a horse with a french link snaffle!