An iron back chair has a wooden seat frame but the back/arm is formed using iron rods. This means that all the canvas, padding and material has to be hand sewn in place, using metal skewers to hold materials in place so they can be sewn tightly in place.
Below are pictures of the various stages of recovering an iron back chair. The quality of the pictures is not great, as they were taken on my phone camera as worked progressed (should have been more organized and had my proper camera).
Quite often there are several layers of fabric on the back of the chair, where previous re-coverings have been done by upholsterers either too lazy to remove the cover or more likely they don't know how to do these and just attempt to fix the new cover to the old. Also in most cases they never replace the back canvas and half of the stuffing is falling through the frame. To date the record for number of layers of covers left on is 5 and the canvas was completely rotten.
On this chair the previous upholsterer had filled in the centre of the back with felt and then tied on a canvas to hold it in position, then covered it. The customer and the antique shop she brought it from, where unaware that this was a iron back until all the extra padding was removed showing the lovely shaped back of the chair