Err. I'm trying to remember what site I had to do this for!
...Time passes...
Okay found it, we'll use it as an example.
If you look at the homepage (http://gigajam.com/) you'll see the site needed four main sections, one for each of guitar, bass, keyboard and drums. Now when you get into those sections I wanted a different main menu for each of the instruments. This is the tabbed menu right at the top. If you go into any of the instrument "schools" you'll see it change.
Now the code we've been discussing that outputs the menu is a function called wp_nav_menu. You're theme will probably already have a call to this function in your header file.
You can learn more about wp_nav_menu on its codex page.
What is happening with the code as discussed above is that I am adding the following parameters to the wp_nav_menu call that was already in my header.
`'menu' => get_post_meta( $post->ID, 'MenuName', true)
If you compare that to the codex page you can see that I'm passing something into the menu argument. What's being passed in is the result of the call to get_post_meta(), which in pulling the value of MenuName out of the custom field for any given post/page.