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If you are talking about the bridge washer, it helps clamps the stem in the tube and helps support it, keeping it from being pulled out. also because of its shape, pointed ends, would help to keep the stem from turning when the outer nut is screwed down. The pointed ends would bite into the tire.
The stems have flats on the sides that match the shape of the hole in the bridge washer. This link shows how the stems were replaced in tubes. Model T, A and many others were the same. Vulcanized metal stems would use the same clamp for the same reason. Rubber stems don't need because they are molded as part of the tube and would only be putting the cap on.
http://sheepisland.com/cars/tech/metal_stems/