A long long time ago, in the System 7 days when Unix was shiny and new it was decided that in /bin would go the binaries, /lib the libraries, in /usr would go the users' homes and everything else would go in... /etc. That's what it meant back then, "et cetera". When applications needed configuration files they often put them in their own additional hierarchies but the users complained that trying to find those files was annoying; they wanted all those files in one directory and /etc was the only place that fit the bill.
After a while the users started compiling their own binaries and they needed to put them someplace other than /bin, so as not to confuse them with the system ones, so that's where /usr/bin came from.
Because /usr became a standardish place which could be used for user-installed stuff, it was more and more populated with things started by users but a lot of those were adopted by systems, so after a while users' homes were moved into /home to segregate the humans from another directory known for system stuff.
/var was born out of the needs of diskless workstations. Into those days, you could boot a machine without a disk; they would load their kernel over NFS and then mount the / and /usr filesystems read-only from a central remote server. It made sense since all the operating-system files were identical on all workstations, so they all mounted the same shared filesystems. But you still needed at least one filesystem where the workstations could read & write their own files separately since this stuff was "variable" between workstations, /var was born.
Boy I'm old.
