The Avatar Relics are four toys that belonged to all the previous incarnations of the Avatar.
The Avatar Relics are ancient toys that have been passed down from Avatar to Avatar in the cycles of the World of Four Nations which consist of a toy turtle, a fan, a drum, and a monkey. Soon, it became a test in order to locate the next Avatar when the previous one passes on. The test involves placing the four toys in a group with dozens of other objects and asking children in the cycle to pick from them. The one that chooses the four toys is deemed to be the new Avatar and is told at the age of eighteen of their role in the world. The test was not given to Avatar Korra since the ancient toys were more than likely destroyed during the 100 Years War as well as Korra demonstrated the ability to bend three elements at once at the age of four.
One should note that this process is identical to the process in Buddhism where the reincarnation of the Dalai Lama is located. High Lamas in Buddhism use this as a test, asking a child to pick from a series of artifacts to see if they choose what belonged to their past lives.