vat tax

Short answer: no.

Slightly longer answer: You can receive the VAT back on goods that you export, unused, from the EU (with a minimum spend requirement.) You cannot reclaim VAT on goods consumed in the EU or services*.

*Exceptions to this are business expenses incurred by a VAT registered company (but that would be an even longer answer.)

I don't want to sound too stupid but what is a VAT?

Value Added Tax

Basically it's sales tax.

The main practical difference for Americans is that the EU requires it to be included in the ticket price rather than ambushing you at the till as in America.