A transition occurs when changes in a package require alterations to several other packages which depend on it. To do this, many packages using the package are updated, either being recompiled or updated to a new version; packages blocking a transition might be removed from testing so it can complete. Transitions can become very large and complex, involving tens or even hundreds of packages.
Transitions are coordinated on the debian-release list. There is a page at http://release.debian.org/transitions/ summarizing active/planned transitions. Teams/ReleaseTeam/Transitions describes how to request and perform transitions.