The Moment

The Moment, previously called the Eye of Discord, was the most powerful and most dangerous weapon in all of creation, described as the Galaxy Eater, which the War Doctor intended to use to end the Last Great Time War when he felt his people had gone too far.

Abilities
The Moment was capable of destroying Gallifrey, the Daleks, and whole galaxies within a single moment, hence its given name.

Additionally, the Moment was able to create tears in the fabric of creation called time fissures that would allow people and objects to pass from one time period to another, possessing a trans-dimensional awareness of the past and future. This ability could also circumvent time locks, which normally prevented people from travelling to important eras of time that were otherwise sealed off. It also had a sentient interface with telepathic abilities, enabling it to read the thoughts and memories of those who intended to use it.

The interface also had the capacity to take the forms of others, such as Rose Tyler, as a holographic projection. As it was a Time Lord construct, it was not limited to a linear grasp of time and space — it could select the forms of people from an individual's future they had yet to meet. However, when trying to tell the past and future apart, the Moment tended to get the two mixed up.

The Moment could also change appearance from a box full of gears to a box looking station with a big blood red ruby button on a stalk, with a base similar to the shape of a rose petal. (TV: The Day of the Doctor)

History
The device was once known as the Eye of Discord and was created by Time Lord scientist, Roppen. Rassilon later employed Roppen to redesign the device to be deployed against the Nestenes. The device gave Rassilon a brief encounter with his future selves before Rassilon activated it and destroyed all the Nestenes in the Illia galaxy. He then placed the device in the Omega Arsenal for safe keeping. (PROSE: Pandoric's Box)

According to the General, the Moment was the final creation of the Ancients of Gallifrey. It had an operating system so sophisticated, so advanced that it had become sentient and developed a conscience (hence why it was never used, as the Time Lords feared its moral judgement). When attempting to initialise it, the War Doctor expressed unfamiliarity with the Moment's controls and operating system. (TV: The Day of the Doctor) The Moment interface recalled that there were no Daleks in her day. (PROSE: The Day of the Doctor)

Usage by the Eighth Doctor
According to another account, the Eighth Doctor created the Moment from a modified Key of Rassilon and De-mat Gun during the Time War. (COMIC: The Forgotten, Don't Step on the Grass)

The Doctor activated the Moment to destroy Gallifrey, destroying both the Daleks and the Time Lords. (PROSE: Doctor Who and the Time War) By using the Moment, the Doctor time-locked the war, making it theoretically impossible to reach via time travel. (COMIC: Don't Step on the Grass)

Usage by the War Doctor
Until the Doctor stole it, the Moment had been locked away along with other forbidden weapons — collectively known as the Omega Arsenal — in the Time Vaults. (TV: The Day of the Doctor) It was kept in the deepest time vault, Time Vault Zero, for billions of years. (PROSE: The Day of the Doctor) While all the other weapons were used against the Daleks during the course of the war, the Time Lords refused to use the Moment for fear that it would punish anyone who did so. When conversing with the War Doctor, the Moment warned him there would be consequences for him if he followed through with his plan. The War Doctor replied he didn't care as he had no intention of living past the war's end. The Moment responded by telling the Doctor his punishment would be to live, burdened with the knowledge and guilt of his actions. (TV: The Day of the Doctor)

Supposedly, when the Doctor used the Moment, he destroyed Gallifrey, the Daleks, and the Time Lords. (COMIC: Sky Jacks) As the Ninth Doctor later stated, all the combatants of the Time War had burned and were "wiped out in one second". (TV: Dalek) The Partisan informed the High Council that the Doctor "possess[ed] the Moment, and [would] use it to destroy Time Lords and Daleks alike," while the Chancellor explained that the Visionary predicted that the Time Lords would die on the last day of the Time War. (TV: The End of Time)

However, the Doctor later learned that his memory was not entirely accurate. When the War Doctor had attempted to activate the Moment, its interface had appeared to him in the form of a face from his future. It gave him an opportunity to change the outcome of the Time War, by involving two of his future selves, the Tenth Doctor and the Eleventh Doctor, allowing him to see the future and later providing an opportunity for the future Doctors to join him as he prepared to trigger the Moment. When the advice of Clara Oswald prompted the Eleventh Doctor to remember his vow as the Doctor, he deactivated the Moment, informing his past selves that the three of them could find another way. Together, with help from their previous incarnations and the Twelfth Doctor, the Doctors were able to devise a way to freeze Gallifrey in time, while allowing the Daleks to destroy themselves in the crossfire. Thus, Gallifrey and the Daleks still vanished, and history was preserved, but the Doctor was ultimately able to prevent the genocide of his own people. The War Doctor and his future incarnations were unable to retain the correct memories until the timeline caught up with the Eleventh Doctor. (TV: The Day of the Doctor)

After the Time War
During a conflict between the Time Sentinels and the Tenth Doctor, the Moment, once again taking the form of Rose Tyler, telepathically contacted Gabby Gonzalez and granted her the knowledge she needed to defeat the Red TARDIS that had taken over the Time Sentinels. It intervened directly and rescued Gabby moments before her imminent death and sent the Twelfth Doctor to save her. (COMIC: The Good Companion)

The Moment had one conversation with the Thirteenth Doctor, spread over two locations. The first was in Henry VIII's third-favourite garden, where the Doctor asked her about the lesson she wanted to impart to him when he saved Gallifrey. The Moment replied that, like with any relationship, she didn't want to be used. Later, when the Doctor stood in a fountain at the heart of the Villengard banana groves, the Moment told her that she helped because the universe needs the Doctor, and at that point in his life he was in danger of stopping. (PROSE: The Day of the Doctor)

Alternate timeline
In an alternative timeline, the War Doctor used the Moment to destroy the Cybermen. (COMIC: Prologue: The War Doctor)

Behind the scenes
In AHistory, Lance Parkin suggested that the Time Lords built the Moment for the War in Heaven but only used it during the Time War.