This post to the BusyBox mailing list from back in 2010 was a fun read to get the backstory on bin, sbin, usr/bin, and usr/sbin.

You know how Ken Thompson and Dennis Ritchie created Unix on a PDP-7 in 1969?
Well around 1971 they upgraded to a PDP-11 with a pair of RK05 disk packs (1.5
megabytes each) for storage.

When the operating system grew too big to fit on the first RK05 disk pack (their
root filesystem) they let it leak into the second one, which is where all the
user home directories lived (which is why the mount was called /usr). They
replicated all the OS directories under there (/bin, /sbin, /lib, /tmp…) and
wrote files to those new directories because their original disk was out of
space. When they got a third disk, they mounted it on /home and relocated all
the user directories to there so the OS could consume all the space on both
disks and grow to THREE WHOLE MEGABYTES (ooooh!).