What does "puddling" mean?

Puddling: (Metal.) The art or process of converting cast iron into wrought iron or steel by subjecting it to intense heat and frequent stirring in a reverberatory furnace in the presence of oxidizing substances, by which it is freed from a portion of its carbon and other impurities. Puddling furnace, a reverberatory furnace in which cast iron is converted into wrought iron or into steel by puddling.