To attach a country to a zone, go to International > Locations > Countries, edit the country and select the zone.
Your PrestaShop installation must know all existing countries in order for your customers to clearly indicate where in the world they live.
There are roughly 200 countries in the world, but PrestaShop has 244 registered. This is because some countries include overseas regions that are part of the country proper.
For instance, the French overseas departments (Guadeloupe, Martinique, Mayotte, Reunion, and French Guiana) now have equal status to mainland France. Likewise, Alaska and Hawaii are US States in their own right. Still, sending a package to Guadeloupe does not mean sending it to France, at least for the shipping fees. Therefore, the list of prices in PrestaShop separates the country from the region.
By default, only your own country is enabled. You should enable them one by one, as needed for your customers. If you are unsure which to enable, check your stats to see the countries with most visitors.
At the bottom of the list, the "Country options" section allows you to only display in your front office the countries that your carriers cover. We recommend that you enable this setting, as it prevents customers from having to scroll through all the country names to find their own.
To attach a country to a zone, just open configuration for the country in question. Then click in the Zone field and select the new zone you have created.