Another term borrowed from Microsoft's project management philosophy, ZBR is where the end really begins.
It means Zero Bug Release, though it doesn't mean shipping a bug-free game...
As a project is coming to an end, the number of bugs in the database should have a tendency to get lower and lower as the bug fix rate is higher than the bug report rate.
When the bug count reaches 0, the project enters a phase called the Zero Bug Release. It means that the bug database should have 0 unresolved bugs by the end of the day (keep in mind that QA is still reporting bugs).
That's the theory. As this definition is somewhat impractical for developers, especially since development and QA teams can be in different time zones, The definition is usually altered as follows:
No unresolved bug should be more than 24 hours old.
As part of the general effort of making the project shipable, this usually means that developers are asked not to leave the office without having fixed all the bugs they were assigned. But more importantly, depending on how far behind the project is (if at all), it means that the bug cull becomes more and more aggressive. QA keeps on entering bugs as usual, but production occasionally intervenes to say "No, we're not going to fix this bug" (or at least, not for this release).
This time of the project is usually the stage of a continuous quarrel between the dev team who wants to make the best game possible, and the producers who want to get the game out the door (because a great game is useless if nobody can play it).