The three Tri-ni-set elements each have a unique ability, granting them a special power. The Vongola Rings' ability is the miracle of the Vertical Space-Time Axis.
This power allows the Vongola to move through generations down the Vertical Space-Time Axis; this means the Vongola traditions can be passed down, from the past to the future.
An example of this miracle is the Vongola Trial, which occurs when the Vongola successor is in a near-death situation; he is given a test of resolve by his predecessors to see if the successor has what it takes to lead the Vongola. Giotto, the first Vongola Boss, explains this by saying that all the Bosses' hours have been engraved into the Ring. The current Vongola boss can also communicate with his predecessors, whose wills have been sealed in the ring.