Iron plates belong to the group of so called ferromagnetic materials which are attracted by magnets. Moreover! Plates in contact with the magnet themselves become magnets. So, the chain- bridge is nothing else but a row of little magnets that are connected to each other by their opposite poles (this way there is attraction between them).
Permanent magnets (rod magnet, horseshoe magnet) are only one type of magnets.
Another type is electromagnet, which is based on the principle that an electric current produces a magnetic field around itself. This is applied in cranes that are used to lift huge loads of metal trash.