Debian's 'production' release.
Stable refers to the libraries and APIs not changing, rather than how likely it is to crash (although Debian Stable is very unlikely to crash).
The current version of stable is code-named 'Woody' (3.0r1) as of 11/8/2003.
Debian testing every so often goes through a feature freeze, has all the bugs worked out of it, and then is released as stable. After that, only security updates (backported to the versions of software IN stable) are released.
Stable is as stable suggests. You'd have to try hard to break it.