Initially, they were produced by Sheffield cutlers as large flat serving knives with a decorative shape based on the outline of a fish. The tip is the snout, the first bulging curve is the head, and the rest is the fin on the back. The tip proved useful in delicately prising out bones from the soft cooked flesh, while the broad blade was used to lift portions of the fish onto a plate without breaking it up. (And is why they sometimes have an off-set handle, so the blade can be slid under the fish more easily).
They were then made as table fish-knives. These quickly became popular among the rising middle classes in Victorian times, who wanted to prove that they knew all about how posh people should live. (Actually, the upper classes traditionally ate like pigs, having nothing to prove!) But their shape does make them useful for removing any bones from what's on the plate.