Does anyone know what the favorites section under the ME tab is for and how to add to it?

I would think it is for saving posts which you would like to go back to fro reference. But I can't find how to save anything in there either.

As Palladous mentions, it is for tagging posts that you may wish to reference in the future.  How to save to it?  Go back to your post #1 in this thread, there is a yellow button with a box in it at the end saying "favourite".  Click this, it will add it to your favourites list.  Simple.  Be aware the forum experience is different if you use a mobile device rather than using a desktop/laptop computer.