The FBI calls it Telephony Denial of Service (TDOS). It is a new and growing kind of security attack that is not centered around VoIP itself but that uses VoIP to better do the job. The operation is carried out in two parallel moves - on one side, a genuine attack is done on a person's interest in a bank, financial institution or other company; on the other side, the person's the person's phone line is flooded at the same time with 'spam' calls in order to block other calls from coming in. That last part is technically called a denial of service. Since verification methods most commonly used by banks and other institutions involve phoning the person for confirmation and detection of attacks, that route would be closed and the attack would be undetected and subsequently successful.
The role of VoIP in it isn't essential, but important. In fact, VoIP is the factor that is causing this kind of attack to grow. The flooding calls could have been done with any phone system, but VoIP makes them cheap.
A number of measures is being taken by the authorities and a number of precautions can be taken by you, users, like notifying your bank or telephone company of any abnormal phone activity on your line. Read more on that in the FBI's release.