The Verified by Visa security program is part of the authentication process by WorldPay, our credit card payment processor. It is perfectly normal, if not an additional pain, but it is there to improve online security such that your card cannot be used by a 3rd party online (the most common source of fraud) even if you lose it. More details are available at https://usa.visa.com/personal/security/vbv/index.jsp

If you are concerned about the entry of the password without identification, please be assured that this is perfectly safe. Your authentication was in the entry of your credit card details (credit card number, cvv, name, billing, etc), which you got correct as you had the physical card and all information entered are encrypted via SSL between your browser and the payment processor. Verified via Visa is simply a 2nd layer of security that is added now that Visa 'sees' you using your card for online transactions.

After setting this password, your card will be more secured against online fraud (only for merchants that support this program) even if you lose it. For example, if someone picks up your card or steals it, he will not be able to purchase anything at iStyles or any merchant that supports this program as he will not know your verified your visa password.