A stage tarball is an archive containing a minimal environment. For example, in Gentoo Linux there are 3 stage tarballs : stage1, stage2, stage3. Sometimes you will see these written as stage 1, stage 2, and stage 3. Funtoo's and Gentoo's official installation method uses stage 3 tarballs.
Stage4 tarballs are user generated stage 3s with goodies attached to them. Stage 4 tarballs contain utilities users deem essential. Some users make stage 4 tarballs as backups of live funtoo systems.