Destroy any divine entity
It's one of my ribs, dude. Everything can contain the spark of the divine, but this puppy? It's packing enough punch to create life. Or, in your case, destroy God.
Adam's rib was used to create life in the form of Eve. Adam claims that his rib is essentially a Hand of God, having a spark of the divine powerful enough to create life or destroy God. When used with the rituals Jack Kline has completed to strengthen his body and soul, the energy in the rib will cause an elemental chain reaction, fusing Jack's grace and human soul into a "metaphysical supernova" -- causing his body to collapse into a living black hole capable of trapping and destroying any divine entity, including God and Amara.
After Jack passes Adam's test to see if he is ready for the final phase of his plan, Adam has Serafina forcefully remove one of his ribs and gives it to Jack. They tell Jack that the divine energy in his rib will mix with his soul and archangel grace to cause an elemental chain reaction that can't be stopped, turning Jack into a metaphysical supernova, powerful enough to suck in God and the Darkness, killing them.
On the drive back to the Bunker, Jack absorbs the energy in Adam's rib, causing it to melt away in his hand. When they arrive at the Bunker, Sam attempts to stop Dean and Jack from going through with the plan. As the chain reaction continues inside Jack, Chuck is able to escape their trap and reveals he manipulated events to get to where they are, telling everyone that they will have to watch Jack die as his body begins to detonate.