The pressure jerkin was used in conjunction with a Taylor E-Type partial pressure helmet, or P/Q type oxygen mask.
It's purpose is to balance the pressure exerted on the inside of the lungs (by the oxygen flow) by applying equal pressure to the outside of the body using inflatable bladders connected to the same oxygen sypply as the mask / pressure helmet. This was of particular importance if the cabin was to de-pressurise when flying at high altitudes.