Basic Information
Hanging between dogs was a frankly bizarre form of execution, used in medieval Europe and most often specified for Jews who had committed some form of blasphemy or sacrilege against (Roman) Christianity. The condemned was tied between a pair of dogs and dragged through the streets to a gallows, from which all three were then suspended upside down until at least the human was dead. The general intent was for the condemned person to be bitten to death by the infuriated dogs (or at least so badly injured that they died soon thereafter), but there are instances recorded in which the dogs were already dead at the time of suspension, or otherwise not able to complete their mission, leading to the sentence being completed by an executioner with a garrotte or club or merely by the passage of time.
Sources
Something from the other wiki, focusing on its use against Jews.