The "Samulet" is a term that was coined by the fandom for Dean's amulet, who speculated that the amulet symbolizes Sam's love for Dean. It's given to a teenage Dean by 8-year-old Sam in 3.08 A Very Supernatural Christmas and remains very important to Dean, who wears it always until he discards it in 5.16 Dark Side of the Moon.
After Dean dies and goes to Hell, he is resurrected in 4.01 Lazarus Rising and is not wearing the amulet. It's revealed that Sam has been wearing it since Dean's death, and when they reunite, he returns it to Dean, who immediately begins wearing it again.
The supernatural use for the amulet is first revealed in 5.02 Good God, Y'All, in which Castiel claims it "burns hot in God's presence." He take the amulet from Dean, who is reluctant to be without it.
A replica Samulet appears in the musical in 10.05 Fan Fiction written by Robbie Thompson. After Marie says Dean should never have thrown it away, he states "I don't need a symbol to remind me how I feel about my brother." However, at the end of the case, when she gives it to him, he keeps it and hangs it from the Impala's rearview mirror (though it is only shown there for this one episode). It is later seen in Sam's Memory Box in Robbie Thompson's next episode, 11.11 Into the Mystic.
In 11.20 Don't Call Me Shurley, God, in the form of Chuck Shurley shows Metatron the amulet, telling Metatron that he'd never believe where it's been the whole time. God reveals that he shut off the amulet's ability to detect him so the Winchesters and Castiel couldn't find him. At the end of the episode, Dean pulls the amulet out of Sam's pocket. According to the script of this episode written by Robbie Thompson, which explicitly refers to the amulet by the fandom name "The Samulet," Sam retrieved the amulet after Dean discarded it in 5.16 Dark Side of the Moon, and had carried it "all these years. This whole damn time." The amulet is glowing, and it finally leads them to God. In the next episode, Dean puts it in his pocket after God transports them back to the Bunker.
For more information, see the entry on Dean's amulet.