The BREACH attack verbage at http://breachattack.com spells it out fairly clearly, by adding random bytes to all of the HTTP responses, it makes small compressed HTTP payloads impossible to determine whether guessed bytes were correct or not (well, depending of course on the size variable of the random bytes added).
> Could you comment on how integrated the TLS stack is with the webserver?
The TLS layer is entirely separate from the webserver layer. I built the epoll, TLS, SSH, webserver and client as "IO layers", such that they can be stacked together arbitrarily (imagine epoll/IPv4 listener -> TLS -> SSH -> TLS -> Webserver, perfectly doable, albeit a little nutty).