When any internet user goes to mailman.cchmc.org, they see a list of the mail lists that have the "List identity" setting set to  "show list on index page"

What is the purpose of the list index page

The list index page is usefully if you want users to find your mail list, but do not know the name.

What does it mean to have my email list public on the list index page

If someone one clicks on your list on the  list index page then they see the info about your list, and can even request to be on your list.  This does not mean anyone can add themselves to your list, it just means they can submit a request to be on your mail list, and then that process is handled by your list settings. I.e do you allow anyone on the list, or do they have to be approved by an admin or moderator etc..