Good question! This peeler isn't just for potatoes. When this was made, it was popular to "french" green beans, meaning slice them into long thin strips (this is where the name "french fries" comes from). The horizontal slats are blades. You push the end of a green bean through, then grab the strips that poke out the other side, and pull the rest of the bean through, slicing it into long thin strips.
I think most people know this, but on the other end is a rounded blade meant for gouging out the eyes (lol) of the potatoes you're peeling. I don't use the frencher but I do use the eye gouger.