Eye of Agamotto

"What is happening?" "Since you gave Kaecilius power from your dimension, I brought some power from mine. This is time. Endless, looped time."

- Dormammu and Doctor Strange

The Eye of Agamotto is a powerful relic created by Agamotto, the first Sorcerer Supreme, to contain the power of the Time Stone inside it. It has been passed down the long line of Sorcerers Supreme that followed him. The Eye has the ability to manipulate the flow of time and was used by Doctor Strange to fight Kaecilius and Dormammu and restore the Hong Kong Sanctum. It was placed back in Kamar-Taj until Strange could learn how to control it.

Creation
The Eye was created by Agamotto, using the Time Stone as a component to allow the user to safely wield it without directly touching it and suffering the adverse effects of touching an infinity stone. The container was created in the shape of an eye, hence its name. The mystical properties of the relic, as well as the spells and gestures necessary to use it, were studied by the writer Cagliostro, who wrote them down on his personal grimoire. The Eye remained in Kamar-Taj where it was discovered by Doctor Stephen Strange.

Strange's Training
"You weren't manipulating the space-time continuum, you were breaking it!"

- Wong to Doctor Strange

Having read one of the passages in the Book of Cagliostro about the Eye, Doctor Strange put on the pendent and tested its power on an apple, forwarding and reversing time on the object. He then used the Eye's power on the book, discovering and reading the stolen passages about the Dark Dimension and Dormammu. However, he stopped using its power as it began creating different alternate timelines, which Wong and Mordo warned against, because it could destroy the natural order.

Battle at the Hong Kong Sanctum
Strange later used the Eye to rewind time in Hong Kong, restoring its Sanctum, and bringing Wong back to life, until he was stopped by Kaecilius, causing all of time to stop before the Sanctum could be restored, thus allowing the Dark Dimension through. Strange flew into the Dark Dimension and activated the Eye.

When he confronted Dormammu to parley, Dormammu killed him, but the Eye's power trapped them both in a time loop that would restart every time Strange died. Dormammu finally relented and accepted Strange's terms, withdrawing his attack on Earth and taking away his Zealots.

With Dormammu gone, Strange returned the Eye to its place in Kamar-Taj feeling he was not ready to wield it yet. Wong agreed, stating that walking around with an Infinity Stone in plain sight is a bad idea.

Capabilities
"Temporal manipulations can create branches in time. Unstable dimensional openings, spacial paradoxes, time loops! You want to get stuck experiencing the same moment over and over again forever, or never having existed at all?"

- Karl Mordo to Stephen Strange

Being the container of the Time Stone, the Eye of Agamotto allows its wielder to use the Infinity Stone's power without having to physically touch it. The eye itself is usually closed and must be manually opened in order to use the stone. It seems that using Eldritch Magic is required to tap into the stone's power and harness it in the form of spells. According to Wong, wielding the Eye without mastering its powers can very well kill its wielder.

The Eye's main use is the ability to control the flow of time, be it on a small or massive scale. In a smaller scale, the Time Stone allows the user to turn something back to its previous state or accelerate its time in order to apply changes that have not happened yet. At a large scale, the stone can rewind time to undo entire events, to the point that doing so can even bring a dead person back to life by rewinding time to a point prior to their death. If the user is interrupted while rewinding time, time freezes until the user resumes the spell.

The Eye can also be used to set up a time loop, resetting its state and repeating an event infinitely until the wielder stops its effects. It appears skilled sorcerers, or perhaps users of powers from the Dark Dimension can to an extent subtract themselves to the effects of the stone, stopping the time reversal affecting oneself or noticing that one is stuck in a time loop.

It is noted by Wong and Karl Mordo that the use of the Eye is contrary to the natural order of things, and is extremely dangerous as it can break the flow of time and create alternate time lines. With Wong's approval, it was placed back on its pedestal by Strange until he learns how to properly harness its powers.

Trivia

 * In the comics, the Eye of Agamotto is one of three eyes created by Agamotto, placed into the care of Eternity until given to Doctor Strange in order to battle Dormammu. It is used for order or "white" magic only. It does not respond to an evil user's commands, and can only be utilized by a magician of a pure heart and clean soul.
 * Doctor Strange director Scott Derrickson said the Eye of Agamotto from the comics was too powerful to be used in the film.
 * This is the second Infinity Stone not to be used to destroy a main antagonist during its first appearance, first being the Aether. However, it is nonetheless instrumental in defeating both Dormammu and Kaecilius.