There were no shortage of mysteries in Avatar: The Last Airbender, but eventually most of them saw resolution. Whether it was the fate of Zuko's mother or the very origin to the Avatar Cycle itself, the franchise has gone to considerable efforts to answer the questions it raised at one point or another, be they in the comics, The Legend of Korra or in bonus content. But one mystery set up in the original series' first season still lingers, haunting viewers with its sparkling eyes and evading any answer: What was going on with that monkey statue?
When the item first crops up in "The Waterbending Scroll" it seems to be a totem of great significance. While idly searching through a shop of curiosities offered by a band of pirates, Katara stumbles across the statue and it has a mesmeric effect on her. The stone statue of a monkey baring its teeth is bejeweled with ruby eyes and a matching necklace, drawing in her gaze. The young Waterbender snaps out of it a moment later once she and Aang find the episode's titular scroll and then that item becomes the narrative focus, leaving the monkey statue to stew in the background.
There it remains when Iroh and his temperamental nephew Zuko come across the shop. Much as it did Katara the statue draws in Iroh's focus and he calls it "handsome" and says it would look "magnificent in the galley," but yet again the plot meanders away from the statue as Zuko follows a lead from the pirates he can use to hunt down the Avatar. The implication is that Iroh purchased the statue off screen given that it next shows up in "The Blue Spirit" in Iroh's possession, serving exactly the function he first brought up for it by beautifying the galley of Zuko's ship.
Those two episodes are the only time the bejeweled monkey statue shows up in the first season. While it initially seems to be built up as something important with quite possibly hypnotic powers, it fades off into the background where it almost becomes just a cute detail that serves as a throwback to its prior mention. The first season ends with the same pirates who sold the statue as a curio returning to try to assassinate Zuko by blowing up his ship. Although the assassination attempt is unsuccessful, the ship was destroyed, and assuming the statue remained aboard, that was seemingly the end of its fate.
While its fate seemed settled, the statue somehow popped up again in Season 3 -- only this time the statue was in the Gaang's possession, and at a time that seemingly makes no sense. Appearing as a small detail in "The Runaway," the statue sits among Team Avatar's possessions. The odds seem almost monumental that the statue could find its way into their possession, necessitating its survival from the ship's explosion, the journey from the North Pole to the Fire Nation and then finding its way into the interest of whoever among the Gaang purchased it.
There was never any reference to Iroh giving the Gaang the item, and indeed most of Team Avatar's possessions were previously lost in Season 2 when Appa was stolen along with the saddle that held most everyone's possessions. The most sensible explanation is that the pirates who originally sold it pilfered it from Zuko's ship prior to their sabotage and made their way southward ever since. But why would the show's creators include such a small and seemingly insignificant detail?
The best answer is in what the monkey represents. The episode it reappears in revolves around Toph and the crew's various schemes to increase their fortunes as they build up a reputation in the Fire Nation for scamming local buskers and gamblers out of their money. Katara, previously enamored with the statue when she saw it in "The Waterbending Scroll," admonishes her teammates for their misdeeds in the same scene where the statue reappears. Not long after, hurt by their accusations that she's overly maternal and boring, Katara decides to instigate the biggest scheme yet along with Toph. This harkens back to when the statue previously first appeared just before Katara's theft of the waterbending scroll.
The statue, hypnotic to Katara when he first saw it, represents a dark temptation for the Waterbender her typically moral nature struggles against. The statue's circuitous journey back to her is typical of Avatar's mythic storytelling, as fate itself conspires to both warn and tempt Katara. With said meaning in mind, its presence transforms from a meaningless Easter egg into yet another display of the show's intricate and masterful storytelling. Much like the teddy bear's eyeball in Breaking Bad, the monkey statue is one of Avatar's most potent symbols, and it manages to be one with a greater degree of subtlety.