A sequence of builds interconnected in some way or the other.
A Build Chain is specifically a Teamcity notation. As suggested by Teamcity - It is normally used to run interconnected tasks linked by snapshot dependencies. A build triggered on a configuration would trigger other dependent builds like a chain reaction.
A common scenario could be running the tests on multiple platforms or deploying the application after compilation to multiple machines.
Other scenarios could be triggering a project build when a dll in the upstream project has changed.
There are ways to achieve this in other tools such as Jenkins, Maven etc as well. A nice post on this using Anthill Pro is here.
