The /etc directory traditionally contains most of the system configuration files: XF86Config and the whole /etc/X11 directory, /etc/rc.d for initialization files, etc.
The /home directory stores all files belonging to the multiple users who have accounts on the system. By default, Linux also stores the files for httpd and ftpd under the /home directory, which is something other flavors of UNIX do not do.
This directory contains all the system libraries that are used for the Linux applications in order to run.
Whenever there is a crash in a Linux system, fsck will run after you restart the system and will check for corrupted files. If it finds anything, it will dump them here.
This directory was created so that you could mount other external filesystems here by default. Of course, you are totally free to mount them wherever you wish, but this is the default directory created for that purpose.
This optional directory is nothing but an inheritance of the good old UNIX days, where all applications that did not come with the operating system were installed here. Red Hat does not tend to use it much, although there are certain applications that may want to install there by default (Lotus Domino R5 for Linux being an example, and even older versions of Corel Word Perfect, as far as I can remember).
The /proc filesystem is actually a virtual filesystem. It does not actually use any space on your hard drive at all, and whenever you run the df command you will notice that it is always completely filled to 100 %. This is normal, since this directory is used by the kernel to dynamically store information about how the hardware is running. If you ever learn enough to check the source code for those little applications that report things like memory usage, you will notice that they usually read their information from this directory. It is certainly a good idea to look around and see what sort of information is held over here, but be extremely careful if you ever decide to change anything.
As mentioned somewhere above these lines, the /root directory is nothing but the home directory for the root account. This is where the system administrator or superuser may store personal files.
The /sbin directory contains system binaries that are so important to the normal operation of the OS that the system would otherwise fail to boot without them.
The are where your system will store temporary files. Many applications will also save temporary files, which is fine except when they may store information that is world readable and of personal character.
The /usr directory contains user binary files (i.e., those binary files that are not specifically set aside in /sbin for system use or for the root account). Perhaps of special interest is the /usr/doc directory, where you will find plenty of documentation on the software installed in your system.
The /var directory keeps spooling, logging, and generic data. You may find information such as the printer and mail spool directories, the various PIDs of daemons that are running in the system (in the /var/run directory most of the time), log files from the mail daemon, the boot process, security messages, etc.