Actually this is not really new. Since 2003 Businesses outside the EU that sell to private (not business) customers in the EU need to pay VAT to an EU member country.

This is called VAT on e-Services.

Most App Stores (except Google Play) took care of this already but if you did direct sales (e.g. via Paypal, direct payments etc) you need to calculate the tax every quarter and pay it to a member state (which will then distribute it to the other states so that you need to do only one payment).

You can read more on the UK government page:

https://secure.hmce.gov.uk/ecom/voes/welcome.do

The main new thing now is that app stores who had a subsidiary in Luxembourg can no longer funnel it through the lowest VAT country but need to split it up according to the customer country.