Jill, if a magnet will pick them up, which is true of most nails, they are made of steel. The kind of steel they are made of is carbon steel. This is because it probably contains between .10 and .50% carbon, .30-.90% manganese, small amounts of sulfur and phosphorus and possibly some other trace elements, with the rest being iron.
Steel is melted in large quantities like 100,000 to 500,000 pounds at a time. With modern equipment, the process of melting 200,000 pounds of scrap metal and casting it into a square 6" x 6" or so can be done in 6 hours. The square, called a bloom, is then rolled, while it is hot, down into wire of the diameter used to make your nails. Coils of the wire are fed into a machine that forms the head on the nail and cuts it off with a sharp point.
That is probably more than you wanted to know about nails but you might want to check the web for more information. I believe that the American Iron and Steel Institute has a site that might be of further help.