As far as which directory is in which location in relation to one another, this is the best descriptions I've seen to date:
The root directory is the entrance hall to your house. Your home directory is your bedroom. Everyone can go into their own bedrooms, but only you can go into your bedroom.
So basically, according this the above, the root directory contains all user accounts within an operating system. Those user accounts have home directories that are sectioned off based on users.
I think your confusion stems from the fact that the word "root" is used haphazardly when referencing places in operating systems. For instance, take a look at another description of what a home directory and a root directory is:
The simple answer is that the “home directory” is the head or “root” of the naming tree of where a specific user places her/his files and is traditionally the directory that the OS places you when you login and forks your shell. The term “root directory” is the name of the head of the entire hierarchical namespace for any UNIX based system.
Do you see how they say the home directory is the root of a user account? Right there - that's what's confusing to a lot of people. People out there should be more specific when using the term "root." For us non-admin types, our heads get bent out of shape.
If you're a server admin, you'll have access to everything on that server, root directory included. You'll also have access to all user home and user directories. If you're just a user who rents out a piece of a server though, like those who use shared hosting accounts, you won't have access to the root directory. You'll only have access to your own home directory.
Here's what Wikipedia says about these directories:
A home directory is a file system directory on a multi-user operating system containing files for a given user of the system. The specifics of the home directory (such as its name and location) are defined by the operating system involved; for example, Linux / BSD (FHS) systems use /home/<username> and Windows systems between 2000 and Server 2003 keep home directories in a folder called Documents and Settings.
To make things easier to remember, just think about the fact that users can go home. That's where all their stuff is. It's the folder that's theirs. Admins can go anywhere, including someone's home. They own the lay of the land. Other users can't go to someone else's home and all users can't go to the root. Take a look:
Users are allowed where it's bold.
Server and system admins are allowed where it's bold.
Of course, the directory structure above is only meant for illustration purposes to help the novice understand which directory is which.
Does anyone else have anything to add? I'd love to see some more technical insight down below.