If checked, Hudson will discard most artifacts from older builds. Artifacts from the last stable former build (if any) are kept, and also those from the last unstable build if that is newer, and from the last failed build if that is newer.
This option saves disk space, but still lets you safely create permalinks
such as .../lastStableBuild/artifact/...
or
.../lastSuccessfulBuild/artifact/...
or
.../lastCompletedBuild/artifact/...
.
(Since the current build is still running, Hudson conservatively assumes that it might yet fail in a publisher - so it keeps at least one older build's artifacts around.)