Ran across two of these and have no idea what they are or what they were used for. They are a scissor type handle with two solid prongs that latch tightly down into the two troves. Many have thought an early curling iron but the handle would heat up as you heat the prongs.
I did an image search and see several similar, and even a couple of exact matches. The descriptions go from it being an early "electric" curling iron (yeah, my thoughts also!), to early curling iron, to hair crimpers. I'd have to go with hair crimpers. antique curling iron - Bing images
Btw, while it may seem that the handles would get too hot while heating, keep in mind that if heated that much, the tool would simply melt hair. ...I'd rate this design right up there with corsets.