[jeroenhd]

PSD2 is an initiative/set of laws that force banks to have some kind of API available to trusted parties so other companies can access customers' financial data (with explicit consent by the user, of course). This allows the banking app from bank A to work with the bank account of bank B, if bank A implements bank B's API. It also includes some other stuff, like adding security requirements to online payments, like the 3DS system is doing.

Companies that make use of these APIs need to fulfil some requirements so that not just any shitty company can ruin your life by hiring shit developers that accidentally add zeroes to the amount of your transactions.

3DS probably refers to "3D secure", a way to secure credit card payments online. I don't use a credit card for anything but paying for American services so I don't know the details of it, but it seems to be a way to redirect credit card users to the checkout page of their bank so that extra security (like 2FA) can be added to online payments.