A build configuration can be made dependent on the artifacts or sources of builds of some other build configurations.
For snapshot dependencies, TeamCity will run all dependent builds on the sources taken at the moment the build they depend on starts.
For artifact dependencies, before a build is started, all artifacts this build depends on will be downloaded and placed in their configured target locations and then will be used by the build.
Concepts: Dependent Build
Administrator's Guide: Patterns For Accessing Build Artifacts | Snapshot Dependencies | Artifact Dependencies
External Resources: http://ant.apache.org/ivy/ (additional information on Ivy)