What is VAT field that appeared after I entered my card number?

VAT stands for value added tax on services within the European Union. 

If your card belongs to a bank within the European Union, you must own VAT identification number. For more information please enter here: http://ec.europa.eu/taxation_customs/vies/faq.html#item_3

You can validate your VAT ID here: http://ec.europa.eu/taxation_customs/vies/vatRequest.html