Often that part is translated as breath-body or body of breath, pointing to the parts of the body and mind involved with the breathing. I know Nyantiloka translated it like this and Bodhi/Nanamoli did as well. That's because the word kaya ("body", but literally "group") does not have to point only to the entire physical body. A bit more detailed analysis you can find here, by Budhadasa: http://www.buddhanet.net/pdf_file/anapanasati.pdf
I've come to understand it this way and think that's a logical interpretation for a sutta that is called sati of breathing. Also, this subclassification of 'body' pointing to the breath, I think is referred to in the sutta itself by this: " I tell you, monks, that this — the in-&-out breath — is classed as a body among bodies
So you calm the breath itself, that's what it means according to the interpretation above.
Note: Thanissaro may mean something else. As far as I know, the above is not his interpretation.