According to its website, the group buys up consumer debt for pennies on the dollar and then just forgives it. Puff...the debt is gone. The movement is an offshoot of the Occupy Wall Street movement and considers this action a bailout of the 99%.
The group claims to have raised over $240,000 of funds and will purchase nearly $5 million in debt--all of it which it will promptly forgive.
The tax consequences of this transaction, however, are subject to debate. Generally, a debtor whose debt has been cancelled is supposed to recognize as ordinary income the amount of the debt that was cancelled. However, Rolling Jubilee argues that this debt forgiveness is purely meant to be a "gift" to the debtor, which would not trigger any income tax.
Below is a video from the group that explains the basics.