The Vongola Sin is a small vile of liquid that the Vongola Boss inherites every generation as proof that the candidate was officially become the boss of the Vongola Famliglia. It was created by Giotto (Vongola Primo) to leave behind all the past battles of Vongola. The vile resides in a special box with the Vongola insignia enraved onto it, it is then the job of the current Vongola Box to protect it. This item is not mentioned until the Inheritance Ceremony Arc.
During the Inheritance Ceremony, the Shimon Famiglia steal the Vongola Sin. Enma then drips the liquid inside into his Shimon Ring, and thus activating it. With this Enma was able to initiate his Hyper Dying Will Mode. He then proceeds to explain that the "sin" is from the blood of the man that Primo had betrayed - Cozart Shimon, the Shimon Famiglia's first generation boss.