Christoph: He saved his life. Well, he saved his soul. Like, literally. The watch, it's like a -- it's like a Horcrux.
Sam: It's a Harry Potter thing.
Dean: Oh, you would know that.
The actual term for the object is unknown, Christoph Nauhaus referred to the objects as Horcruxes -- a term from Harry Potter referring to objects that contain the soul of a person. Before a person dies, they can place their soul inside an object to remain alive if their body is destroyed afterwards. The object can take a vessel inside another person if that person contains the blood from the family line of the person whose soul will inhabit the body. It will dig into the vessel, deactivate the soul that is already there, and reawaken the vessel as the reincarnation of the person who will take control of the body.
Before he died, Adolf Hitler agreed to have his soul preserved within his pocket watch by Commandant Nauhaus, a high ranking member of the Thule Society. Thule agents were attempting to move the pocket watch to another location until it could be used to revive Hitler when they were ambushed and killed by the Soviets, losing the watch to them in the process. The watch ended up with the family of the Soviet agent, who kept it as a memento. It bounced around to China and Peru and multiple other places around the world until it ended up at an antique shop at Columbus, Ohio, in 2016. The owner of the shop and a woman who wanted to purchase the watch were both murdered by Nauhaus through spontaneous combustion.
Sam and Dean are able to track down a Thule Society member named Christoph Nauhaus who reveals to them their plan to resurrect Hitler, including the fact that the Thule Society keeps track of every one of Hitler's descendants, including Ellie Grant. Wolfgang and his henchman go to retrieve Christoph and Ellie to continue their plans, but are called back as they are battling against the Winchesters after retrieving Christoph. Ellie, who escapes, is later abducted by Commandant Nauhaus.
Commandant Nauhaus infuses Ellie's blood into his body to be used as a vessel for Hitler. The pocket watch is placed onto his chest where it opens the Commandant's chest with four small blades built within the design of the watch. The scar it leaves behind after it disappears inside the Commandant's body resembles a Nazi Swastika. Hitler has an exhilarated and very awkward reunion with Hans, Wolfgang, and Gottfried, the other Thule Society members from his inner circle, who were present with him during World War II before he preserved his soul and took his own life, who are currently present during the reincarnation. Sam and Dean come in to take out the Thule Society members and save Ellie after Christoph, who was sentenced to death by his father, the Commandant, showed them where they are after he escaped. While Hitler is distracted by Sam and Dean, Ellie is able to break free from her restraints and shoot Hans in the head, killing him. Dean kills Wolfgang and Gottfried before moving on to kill Hitler. Dean is able to restrain Hitler and shoots him in the head, which makes Dean very proud of himself. It can be assumed that the pocket watch was destroyed with Commandant Nauhaus when Sam and Dean incinerated the bodies.