A build is a single compile or test run of a particular version of the source code, and is comprised of a series of steps. It is ultimately up to you what constitutes a build, but for compiled software it is generally the checkout, configure, make, and make check sequence. For interpreted projects like Python modules, a build is generally a checkout followed by an invocation of the bundled test suite.
A build factory describes the steps a build will perform. The builder which starts a build uses its configured build factory to determine the build's steps.