It isn't a setting, it is a web part. Do Edit Page - Modify Shared Page
- Add Web Parts - Drag the Area Contents web part onto your page.

Sorry, I'm talking about the navigation links along the left  marging
in the shaded\gradient area. Not the body web part zones where you
can drag web parts.

On the homepage, I have one portal  where the top level areas  are
listed there. I have another where the sub areas of one of my top
level areas are there.

You might be thinking of the portal  Site Map. You can get there by going to http://portal/_layouts/1033/CatMan.aspx?Everything=1 or just by going to Site Settings and then Manage portal site structure.

However, with an out-of-the-box portal, as far as I know, only one area  is listed on the left-hand side (topics? Corporate? I forget).

Anyway, when you edit a specific area or subarea, there is a Display tab that lets you exclude it from portal site navigation, but as far as I know, this only affects top-level areas  that have a presence on the top horizontal navigation component.

The portal  Home is displaying the Topics area  and sub areas. If you are
not using Topics, you can either hide the area from the navigation (in
the area settings) or delete it altogether.

If you are using Topics, you can move the sub areas  to another new area,
then delete or hide Topics. Once you get rid of Topics, the Portal home
page will display the areas for the portal like it does in the top
navbar.

One more note, when you customized your Portal, you may have renamed
Topics to something else. So keep that in mind when looking at your
nav. But the Topics area is the culprit.