Avatar Relics
From Avatar Wiki
These ancient toys are part of an ancient ritual used in identifying the Avatar at a young age. The child is asked to choose from among thousands of relics, four of which once belonged to former Avatars. If the child chooses the four Avatar relics, it is a strong sign that he or she could be the reincarnated Avatar (the logic being that the real Avatar would subconsciously choose the four toys that were familiar). Presumably only children born within approximately a week of the death of the previous Avatar are tested in this way, although those born a little later may also be tested as it is unclear how soon news of the previous Avatar's death would reach the next nation in the cycle.
The four relics represent the different Nations: Air, Earth, Fire and Water. The first one shown is the turtle, symbolizing the Water Tribes. The Fan, for the Air Nomads. The Hog Monkey, for Earthbenders and the Drum for Firebenders. Aang felt that he chose them because they seemed fun, but at least subconsciously he chose them because they were familiar.
It is unclear if this particular method of identifying the Avatar is unique to the Air Nomads, though it seems unlikely given this method is based off the sole real-world way a suspected reincarnation of Tulku Lama is recognized in Tibetan Buddhism. If this is the case then it is probable that the other nations use different artifacts as these particular relics were still in the possession of the Monks over a decade after Aang had been identified as the current Avatar.
It is unknown if the relics survived the war.
