Linux has /usr/local and ~/.local (for gnome and Ubuntu). So what does "local" mean? What is the 'remote' which contrasts with this 'local'?
Does it have anything to do with networks where all the computers share the same system files?
It's typically reserved for "locally installed" applications, meaning stuff you install yourself, not stuff that came with your distro. It's a pretty old naming convention:
http://objectroot.org/articles/brief-history-of-hier/
From https://en.wikipedia.org/wiki/Filesystem_Hierarchy_Standard:
Tertiary hierarchy for local data, specific to this host.
There is no real "remote" counterpart, the correct counterpart is more like "global" instead (meaning functionality that everyone else has, versus functionality that only this local system has).