Here's where I'm starting with a map that uses the map shape role.
Go back to the data table and right click on the column name that has the information you want to use as a label (in my case it's the country name) and select Label/Unlabel.
If you look at the list of column names it should have a little label tag icon next to it.
Select the rows in the data table for the shapes you want to label. Right-click in the area with the row numbers and select "Label/Unlabel."
The rows should have little label tags now, too.
The map should now show the labeled information as well