Blender depends on many libraries. The complete list and the versions in official releases can be found in the Blender repository:
For Windows and macOS precompiled libraries are used. On Linux there is a choice between using libraries installed through the package manager, or to create a portable build with all library dependencies built from source.
Windows and macOS libraries are stored in an SVN repository, and automatically downloaded when running make update. Blender builds with these libraries are portable and can be run on other computers.
Building library dependencies on these platforms is normally only done by platform maintainers.
On Linux, the standard method for most users is to use shared libraries installed through a package manager. There is an install_deps.sh script available to automatically install them on common Linux distributions. See the Linux build instructions for how to use it.
Blender builds made this way are not portable, and generally only run on the computer they were built on.
For building static portable libraries, the Blender repository has a CMake based dependency build system. It builds all dependencies from source with the make deps command. This is the system used to generate precompiled libraries for Windows and macOS, and also used for official releases and the buildbot on Linux.
It has not been tested on many different operating system installs and is mainly used by platform maintainers. Minimal instructions on how to use it are here:
If you need to make a portable Linux build, this is the system to use. Besides the libraries, the glibc version of the system affects portability. Builds will only run on Linuxes with the same or higher glibc version. For that reason official builds are made on somewhat older Linux distribution versions.