- "Temporal manipulations can create branches in time. Unstable dimensional openings. Spacious paradoxes, time loops! You want to get stuck reliving the same moment over, and over, forever, or never having existed at all?"
"They really should put the warnings before that stuff."
- ―Karl Mordo and Doctor Strange
The Time Stone is one of the six Infinity Stones, the remnants of singularities that predate the universe. It has the ability to manipulate time, even in places "beyond" time, such as the Dark Dimension. It was contained inside the Eye of Agamotto under the protection of the Masters of the Mystic Arts, who swore to protect it. Doctor Strange came across the relic in Wong's library and used it to force a bargain with Dormammu.
When the universe was first born, the Cosmic Entities fashioned the remains of six singularities into concentrated ingots which became known as the Infinity Stones. As indicated by its name, the Time Stone held dominion over the forces of time.
The master sorcerer Agamotto fashioned a containment device to better wield its dangerous power. When Agamotto founded the Masters of the Mystic Arts, usage of the Eye became forbidden, though Cagliostro was permitted to study the artifact and eventually wrote how to control the relic in his book. The Masters would subsequently swear an oath to protect the Time Stone with their lives.
Usage by Doctor Strange
During his training a Kamar-Taj, Doctor Strange began to read the Book of Cagliostro and learned of the Eye's full power. Seeking to push himself, Strange donned the Eye and opened it, revealing the Time Stone, first testing its power on his apple before using it to recreate the lost pages from the Book. He was halted by Wong and Karl Mordo who warned that the Eye's powers were contrary to the natural order of things and the slightest misuse could result in an endless temporal loop.
When the Hong Kong Sanctum was destroyed and the Dark Dimension began assimilating Earth, Strange used the Time Stone to rewind the destructive events only to be stopped by Kaecilius before the Sanctum could be fully restored. At wit's end, Strange flew directly into the Dark Dimension to confront Dormammu, trapping the being in a time loop that Strange would only break if Dormammu acquiesced to the human's bargain. Dormammu eventually withdrew from Earth with Strange returning the Eye to its resting place in Kamar-Taj soon after where Wong causally revealed its true nature.
Bruce Banner returned to Earth to warn the planet of Thanos' imminent arrival. After meeting Strange and Wong, the three sought out Tony Stark for his aid who simply proposed destroying the Time Stone to derail Thanos' plans, to which Wong told him of the oath to protect the relic while Strange postulated it might be their greatest weapon against Thanos. As the four debated which action to take, Ebony Maw and Cull Obsidian arrived demanding the Time Stone. While the Earth heroes managed to defeat Obsidian, Maw managed to abduct Strange who revealed he had placed a spell around the Time Stone so that it could only be taken from him if he wished it so. Strange then attempted to use the Stone against Maw only to be overpowered and brought aboard Maw's Q-Ship. Mid-flight, the torturer attempted to force Strange into surrendering the Stone only for him to be slain by Iron Man and Spider-Man. Though Strange wanted to head back to Earth, Iron Man convinced him Thanos would follow the Time Stone wherever they took it and that fighting him on Titan, away from any innocents, was the best course of action. Strange reluctantly agreed but warned he would sacrifice them all for the Time Stone if need be.
Upon arriving at their destination, the three were met by half of the Guardians of the Galaxy. As introductions were made, Strange used the Time Stone to examine fourteen million six hundred and five possible outcomes of their inevitable battle with Thanos. In all but one, they would lose. In preparation for the Titan's arrival, Strange removed the Stone from the Eye of Agamotto and sent it to hide amongst the debris. In the subsequent battle, Thanos, while impressed by Strange's mastery of the arcane, soon deduced that he had parted with the Time Stone given that he failed to use its power against the Titan. When Thanos was on the verge of killing Tony Stark, Strange bartered the Time Stone for his ally's life. Inserting it into the Infinity Gauntlet, Thanos promptly took his leave to collect the Mind Stone.
Upon arriving in Wakanda, Thanos effortlessly made his way through the resistance but was too late to stop Wanda Maximoff from destroying the Mind Stone. Unfazed, he simply used the Time Stone to resurrect Vision and recreate the Mind Stone, allowing him to complete the Gauntlet whereupon he was stabbed by a vengeful Thor. In spite of his wound, Thanos managed to use all six Stones to wipe out half of all life in the universe. On Titan, Stark questioned why Strange had given up the Time Stone who cryptically stated there had been no other way before he vanished.
As the Infinity Stone that represents and governs over the flow of time, the Time Stone is among the most powerful artifacts in all existence. Due to its power, it cannot be held and used by anyone not powerful enough to withstand it, thus forcing Agamotto to create the Eye of Agamotto as a container to allow other sufficiently advanced sorcerers to wield it.
When contained in a device capable of harnessing its power, such as the Eye of Agamotto or the Infinity Gauntlet, the Stone's power uniquely manifests in the form of mystical green runes of energy surrounding the user's arm and wrist. Manipulation of time then occurs primarily through the conjuration of a green, circular mandala made of energy in the user's hand. The mandala acts as a rudimentary "dial", and the manual turning of the mandala with the user's hand enables them to "scroll" both backwards and forwards through time.
Through manipulation of the mandala, the user is able to physically control and redirect the flow of time, and can specifically select the exact area which to manipulate, without affecting those outside its selected range. This can range from a small apple to the entire timeline itself, to the point where Doctor Strange used the Stone to reverse the destruction of the Hong Kong Sanctum before it was consumed by the Dark Dimension, while specifically subtracting himself, Mordo and Wong from its effects.
Due to the selective nature of the Time Stone's power, it could be used to individually alter the timeline of individual objects or events, reversing them to a previous state or sending the object forward into a future state. This occurs regardless of any potential breaches in causality - when Doctor Strange practiced the use of the Stone on a half-eaten apple, sending it forward in time, the apple converted to a fully-eaten, moldy state, despite Strange never physically eating the entire apple afterwards. This implies that the Stone could send objects forwards to a potential future state, that does not necessarily have to occur in the current timeline.
Notably, this disregard for causality also allows for the spontaneous formation or erasure of matter in order to conform with the established timeline. As shown when Strange reconstructed the torn pages of the Book of Cagliostro, duplicates of the pages reconstituted from thin air, without the actual pages, or the one who currently possessed them being physically present, although it quickly vanished after Strange stopped using it as it was not real and only a copy. When reversing the flow of time around the half-eaten apple, the Stone reconstituted the eaten parts of the apple with no ill effects to Strange himself. 
When added to the Infinity Gauntlet, Thanos displays a strong level of mastery and familiarity with the Stone's capabilities, as he was able to harness its unique energy interface to even reverse the destruction of the Mind Stone and death of Vision at the hands of Wanda Maximoff without affecting Maximoff herself and he was also able to perfectly recreate the Mind Stone rather than only making a copy of it, as the Mind Stone retained all it's powers, showing that a sufficiently proficient and knowledgeable wielder can truly recreate even extremely powerful objects that were completely destroyed. This can be attributed to Thanos's skill being considerably more advanced than Strange due to having extensively researched the Infinity Stones for centuries and thus understanding the Time Stone's powers and workings more than Strange ever did.
The Time Stone also allows the user to mentally gaze into the continuum of probabilities, viewing alternate timelines and possible future outcomes at an incredible rate. The Ancient One was able to use it to peer through time and see future threats. Doctor Strange exploited this ability prior to the Battle of Titan, looking through over 14 million alternate futures, to find a way to defeat Thanos.
Even then, the Time Stone's control over causality and probability can easily prove too much for anyone who does not have the required knowledge and ability to use it, potentially resulting in the user's death and a danger to the natural order. Misuse of the Stone's abilities could potentially result in unstable openings and breaks in the space-time continuum, spatial paradoxes, time loops, or even risked completely erasing the user from existence.
However, this can be used to the wielder's advantage - the Stone can be used to deliberately loop segments of time through the formation of a literal energy loop over the wielder's wrist. Upon the wielder's death, the timeline will revert back to the initial formation of the energy loop, allowing the wielder to begin a new iteration with the memory of all previous timelines.
Notably, beings from, or that draw power from, the Dark Dimension, a universe without time, are to an extent, immune to the effects of the Time Stone. The Zealots were able to use their powers to subtract themselves from the reversal of the Hong Kong Sanctum's destruction in order to duel Strange and Mordo, and Dormammu himself retained his memory and awareness between iterations of Strange's time loop (much to his dismay and irritation).
After the Infinity Gauntlet was completed, the power of the Time Stone combined with the other Stones allowed Thanos to kill off half of all life in the universe with a single snap of his fingers.
- In the comics, the orange Time Gem manipulates time; can amplify or reverse aging; and allows the user to see, travel into, and/or change the past or the future.