Dry Ironing
Refers to ironing damp textiles dry as opposed to using a steam iron on dry items.
In both cases one is using the power of heat and water to cause molecules/textile fibres to rearrange themselves and fix the result, however for the most part dry ironing works best on linen and cotton. Indeed pure linen requires the very high heat and steam output of commercial irons (or those close to it), in order to be ironed while dry. Otherwise linen must be ironed moist, whilst cotton only slightly damp.
Being as this may certain cotton weaves still are best "dry ironed" or slighly damp and steam ironed. In general the tighter the weave (percale for instance), usually means results aren't going to be great with steam alone on dry fabric. If you've ever had dress shirts come back from the cleaners/laundry looking like something the cat dragged in, you know this.
Steam ironing was seen as a boone to the housewife since it freed her from having all that damp laundry after wash day (which could moulder), and or having to sprinkle and wait for dry laundry to become evenly moist enough for ironing.
Early books such as the famous Mary Proctor book on ironing showed how one could do a shirt in 4mins, sheets in 8mins and other time savings from using a steam iron versus a dry.
Being as this may, certain textiles should always be ironed with steam. Rayon, polyester, and other man-made fibres benefit from steam ironing in that the moisture protects them from the heat of the iron.
As more and more man made fabrics took over in the household, and steam irons became better designed, "dry ironing" slowly faded away for most.