ls /bin will show you things like ls, sh, csh and the like
ls /usr/bin will show you things like vi, passwd, pkill and the like.
ls /usr/sbin will show you things like sendmail, sshd.
ls /usr/local/bin will show you installed programs, as will ls /usr/X11R6/bin where a lot X related programs are installed, such as xterm.
ls /usr/local/sbin will show things like postfix, apache commands, and other programs that don't come with a base system, but can be considered system programs. (This can often leed to needless debate, but people are used to it.)
Most 3rd party programs (and this goes for tarballs downloaded for Linux as well) install in /usr/local/bin by default.
So, the local in this case, refers to programs which you decide install.
You can find the location of a program with the which command, eg
gives an answer of /usr/X11R6/bin/firefox.
Then, if you do
you get the answer of Bourne shell script text executable.
This means that it's actually a shell script that calls a binary.
Hopefully, this has given enough information without giving so much information that you're confused.