What are the different directories of an Homebrew installation (/usr/local/...) for - homebrew

Question

I am trying to get a hold of the structure of my Homebrew setup and would like to know what these different directories in /usr/local are for:
/usr/local/bin
/usr/local/Caskroom
/usr/local/Cellar
/usr/local/etc
/usr/local/Frameworks
/usr/local/Homebrew
/usr/local/include
/usr/local/lib
/usr/local/opt
/usr/local/remotedesktop
/usr/local/sbin
/usr/local/share
/usr/local/var
Homebrew
contains the Homebrew app
Cellar
contains all the racks someone installs through Homebrew. A rack contains the different versions of an application
But the rest: bin, etc, Framworks, include, lib, ...?

Answer 1

Many of these directories are part of the Filesystem Hierarchy Standard, and so have a standardised purpose regardless of the fact that you're using Homebrew.
My answer is based mainly from hier(7) for directories that both macOS and Linux share, and the MacPorts wiki for more macOS specific answers.
🖥 Non-Homebrew Specific
/usr/local/bin
This is where your standard executable files are stored. e.g. When you type vim into the terminal, the file that's run is stored here.
/usr/local/etc
These are local configuration files. Shell completion files are examples of this (when you hit tab to autofill a command's options).
/usr/local/include
This is where header files are stored that are used by C programs. These contain pre-defined functions.
/usr/local/lib
Object libraries are stored here.
/usr/local/opt
This contains static files, including licenses, READMEs, and install receipts.
/usr/local/sbin
These are executable files that which aren't normally run by standard users. e.g. System programs and administration utilities.
/usr/local/share
This folder contains architecture-independent files. Examples might include documentation and man pages.
/usr/local/var
Files which may change in size can be stored here. Log files are a good example.
🍎 macOS Specific
/usr/local/Frameworks
This is for native macOS frameworks. Python makes use of this for storing the Python app and executable.
/usr/local/remotedesktop
I'm guessing that this stores files from Apple Remote Desktop.
🍺 Homebrew Specific
/usr/local/Caskroom
This directory contains named casks (i.e. applications) e.g. Firefox, Telegram. See the Homebrew terminology page for more information.