If you observe several flavours of unix operating system than you will find some what difference in directory names, but most of the common are explain below...
/bin stands for binary (contains binary files and also contains commands mostly used by users. It is also the default path for command execution ).
/sbin ( this contains the special commands which are generally fired by super user)
/lib stands for library (contains shared libraries used by filesystem and for booting, probably used by the executables in bin)
/proc stands for processes(if you wanna verify just check this director it will contain several directories named in random numbers, that are nothing but process number you can cross check by ps - ef)
/root means root user.( default directory for root user)
/home ( all the non-root users have there home directory under this directory)
/dev stands for device (holds special and device files, if you look in this directory via ls - l command major and minor numbers are also shown in this directory also the device type shown at starting of each line in ls - l result. B means block special device, c means character special device ).
/tmp stands for temporary.( temporary resources required for some process kept here temporarily )
/mnt stands for mount point (mount a temporary filesystem here).
/var stands for variable( it holds variable data, the directory it contains are changing in size every time)
/opt stands for optional (generally third party Software are installed in this directory).
/usr stands for Unix System Resources.( all the system required resources are placed here)
/etc stands for etcetera ( it is also important one, most of the configuration files, user management files, security files and other things are kept under this)