What does "opt" mean (as in the "opt" directory)? Is it an abbreviation?

In the old days, "/opt" was used by UNIX vendors like AT&T, Sun, DEC and 3rd-party vendors to hold "Option" packages; i.e. packages that you might have paid extra money for. I don't recall seeing "/opt" on Berkeley BSD UNIX. They used "/usr/local" for stuff that you installed yourself.

But of course, the true "meaning" of the different directories has always been somewhat vague. That is arguably a good thing, because if these directories had precise (and rigidly enforced) meanings you'd end up with a proliferation of different directory names.

The Filesystem Hierarchy Standard says this about "/opt/*":

"/opt is reserved for the installation of add-on application software packages."

By contrast it says this about "/usr/local/*":

"The /usr/local hierarchy is for use by the system administrator when installing software locally."

These days, "/usr/local/*" is typically used for installing software that has been built locally, possibly after tweaking configuration options, etcetera.

Add-on software packages.

See http://www.pathname.com/fhs/2.2/fhs-3.12.html for details.

Also described at Wikipedia.

Its use dates back at least to the late 1980s, when it was a standard part of System V UNIX. These days, it's also seen in Linux, Solaris (which is SysV), OSX Cygwin, etc. Other BSD unixes (FreeBSD, NetBSD, etc) tend to follow other rules, so you don't usually see BSD systems with an /opt unless they're administered by someone who is more comfortable in other environments.

OPTional

It holds optional software and packages that you install that are not required for the system to run.

It's usually describes as for optional add-on software packagessource, or anything that isn't part of the base system. Only some distributions use it, others simply use /usr/local.