The Piece of Resistance is an extremely important object in The LEGO Movie. A large part of the movie's storyline revolved around it, and was even the original name for the film: LEGO: The Piece of Resistance.
At an unknown point in time, the Kragle, along with its cap, the Piece of Resistance, was found by the characters of The LEGO Movie. At another unknown point in time, Vitruvius hid the Kragle inside a volcano, and its cap in a block of ice underneath Bricksburg. The Piece of Resistance passed out of memory, known of by only a few groups: among them, the Master Builders, along with Lord Business and his robot underlings.
Another unknown amount of time passed until the time when Emmet, after falling through a hole in a construction zone, discovers the Piesce of Resistance. It subsequently glues itself to his back, presumably using leftover bits of glue from its time as the Kragle's cap. Emmet then proceeds to go on a series of adventures, and at one point nearly succeeds in placing the Piece of Resistance back on the Kragle. However, he is thwarted by Bad Cop.
Not long afterwards, Emmet is given the opportunity to place the Piece of Resistance back on the Kragle; however, the Kragle was being held by Lord Business, prohibiting Emmet's attempts. Eventually, though, Emmet convinces Lord Business that everyone should be free to express their creativity in any way, shape or form they wish. Lord Business then places the cap on the Kragle. Moments later, a prophesied explosion takes place, and the Kragle is assumed to be no more.