As stated by BitTorrent (see also the user guide), the secret is a randomly generated key of 20 bytes or more. Simple laws of probability make it virtually impossible to guess. There are four kinds of secrets:
- (master) secrets for read/write access
- read-only secrets
- one-time secrets (both full access and read-only)
- secrets with encrypted peer support for read-only encrypted access
As far as I understand (and stated in this thread where someone tried to reverse-engineer the BitTorrent Sync protocol in July 2013) the latter three types of secrets can be derived from the master secret. In particular this includes a key for encryption of files for transmission between peers. For peer discovery the secret is hashed, so the hash can be used to find peers with a matching secret withing having to make the secret public.
Before further reverse-engineering BitTorrent Sync, keep in mind that the software is closed source and it includes routines to automatically update from bittorrent.com. This implies the company may change details of implementation (and install arbitrary backdoors as well). Nobody can guarantee there is no hidden method that sends your master secrets to NSA, unless the full client source code is opened.