What it says pretty much. Visa sets and asks for a password when you make an online spend. It's a unique password for the Visa splash screen that pops up. Not all websites ask for it.
I guess it's the 3D Secure/Verified by Visa (VBV) password for online payments.
Although I think that I've had such a password on the old (Wavecrest) Wirex card, I don't have on the new one, so if you have it, it may be related to higher amounts of money spent in online transactions.
I think that it's handled completely independent from Wirex (it may be handled by the bank though. Contis?).
It should have been asking first for set a password (obviously) - OR (!!) - the newer 3DS handling is done in many places by sending you an SMS to your phone with the code.