I think you're referring to the recent mastercard hack. (Not Visa)
http://www.securityfocus.com/news/11219

In this case, only card info was compromised. Customer data was not.
Identity theft is not a concern in this case...
Customers are not liable for fraudulent charges...

rcgreen has outlined how the attacker could use the info. Basically sell to various criminal groups who will know what to do with the data. Its unlikely that the attacker themself will be using the data for purchases. Its too risky. They'll most likely sell the card info and move on.

I would assume that they probably already have ties to various organized crime groups BEFORE the hack. Trying to make ties after the hack doesn't make much sense, IMO.