The Shard of the Division was the single piece of the Crystal that flew out when it cracked.
Many trine ago after it had been separated from the Crystal and fell into the catacombs beneath the Castle, both Aughra and Raunip searched for it, however they were unable to determine which of the shards they collected was the one they sought.
Somehow, the shard was retrieved by skekGra the Heretic and urGoh the Wanderer, who hid it inside a weapon they created called the Dual Glaive. After the Second Battle of Stone-in-the-Wood, Brea found the shard after the Dual Glaive was split by SkekMal the Hunter.
Sometime during the Garthim Wars, it ended up at Aughra's observatory, where it was found by Jen during his quest. At first, he had no idea what he was supposed to do with it, but when he and Kira discovered the prophecy on The Wall of Destiny, its purpose was made clear.
After seeing Kira nearly be fatally wounded by the Ritual-Master, Jen inserted the shard into the Dark Crystal, re-uniting the Mystics and Skeksis into the urSkeks, bringing balance back to Thra, and forming the Pure Crystal again.