It's important on this subject to differentiate between "real life" and "D&D."
As others have said, in real life, cold iron is merely iron.
Medieval smelting techniques don't produce iron, they produce high-carbon steel (because the iron ore is smelted in charcoal which obviously impregnates the resulting alloy with carbon).
Not sure where that comes from - that is how medieval smelting techniques prouce steel, but it certainly doesn't preclude the production of iron. The way it happens is that the longer you work the iron, the more carbon gets introduced until you get steel.
Here is a great link on the subject.
In D&D, Cold Iron is a specific form of metal, with a different method of forging. My personal feeling is that this explanation makes little or no sense. Iron melts when iron melts.
In my game, Cold Iron is iron taken from meteoric iron - hence nearly pure, then smelted into form. This was not unheard of in ancient days - Tutenkhamen had an iron dagger in his tomb, and it was probably made from meteoric iron, and hence one of the most valuable items in the hoard. I prefer this solution to the standard ruling.
Why not just have it be regular iron? Because, as Piratecat said to me when I broached the subject a couple of years ago while designing my campaign world and looking for advice, "It's more fun that way." Making strange weapons out of strange stuff is cool, and that's enough reason.