I have come across this issue on several occasions and each time I find myself searching for the solution. I thought to myself, “self, maybe you should blog about this issue so you remember how to solve it the next time you come across it.”
If you are attempting to use the “Import Spreadsheet” app in SharePoint 2013 and you receive the error “The specified file is not a valid spreadsheet or contains no data to import” do not panic. Your spreadsheet is most likely just fine. The issue is with Internet Explorer blocking the functionality. In order to fix the issue you simply need to add your SharePoint site to your list of trusted sites. Go to Internet Options > Security > Trusted Sites and add the URL of your SharePoint site. Don’t forget to remove the check for “Require Server Verification” if your site does not use HTTPS.