'Wrought iron' means 'worked iron' and wrought iron is the product of a blacksmith's hard work. It is produced by heating the metal and hammering it on a forge. This process makes the iron supple, so that it can take on graceful curves, and drives out carbon and other impurities, making the iron more durable. It is a relatively expensive process. Wrought iron ornaments are availaibe but it is rare for large items of garden furniture to be wrought in this manner.
'Iron' comes from the Scandinavian word 'iarn' and has been used since prehistoric times. Because it is harder than bronze, iron was an extremely valuable material. The Iron Age came after the Bronze Age. Blacksmiths work in an ancient tradition, though most of them now use mild steel.