A lot of out of country purchases require this now (Especially train and airfare). I had never heard of it until I tried to book a train in Spain. Visa has the exact same program and calls it Verified by Visa. Oddly, Chase supports the Visa one but not the MasterCard one. Discover and Amex are still trying to come up with a system vendors will get behind; I feel like they'll have the exact same thing soon.

This exists because companies have begun storing credit card information in incredibly insecure ways and it gets stolen by hackers. Without a physical card, you pretty much can only use it on line or to pay a bill over the phone. The SecureCard and Verified passwords are stored by Visa and Mastercard themselves, so a hacker can't* get them and so can't use your card for a transaction that requires this added security.

*If a hacker got them, it would be some mission impossible style stuff and probably involve actual infiltration of a data center somewhere.