Sounds like the issue is that CiviCRM doesn't recognise the contents of your Country column (for some rows).
In the import UI, you should see an option to download rows with errors, and that CSV will report which exact country values CiviCRM does not recognise.
Eg, CiviCRM would accept either
United States (CiviCRM's label) or
1228 (CiviCRM's DB ID), but if the CSV contains
United States of America or
U.S.A, then CiviCRM might not recognise that alternative.
Cleaning this up is usually as simple as a Find & Replace in your import spreadsheet before re-importing. You might then rinse and repeat (
New Zealand) for further countries, or other invalid data that needs cleanup.
To get a working import format, try exporting a few contacts (even if you have to create a few first), then use the resulting CSV as basis for your next import.