Packaging in this sense is referring to grouping the built binaries and other files into a set of installable files that you can install (i.e. the rpm files in Fedora, deb files in Debian and msi files on Windows). These take care of specifying the dependencies and upgrades.
The discussion in TFA is how to group those packages so they are more manageable. For example, a core layer is critical for running the OS (containing the kernel and other essential software), like the projects built in the Linux From Scratch manual.
This then allows those groups to update and release independently of each other. These updates ensure that the packages in the group work well together. That is, you usually need to make sure that gcc, binutils and glibc all work well and update together so they would be in a group together.