It goes on the top of the barrel that screws over my coils and makes contact with the top of the inside of the chimney.
I was rinsing my Nano off last night and accidentally lost it down the drain. I checked the bag of o-rings that came with my tank but the only one that's even close to fitting is just a few mm too big, almost like it's the barrel o-ring for the full size Billow V2.
Anyway, I've been using it without this o-ring and it hasn't leaked, gurgled, or anything. As far as I know, the top of the barrel doesn't even come into contact with any e-liquid.