An ancient and powerful race, the Kin was particularly dangerous for its unique relationship with time; although there was only one Kin, it could travel back along its own timeline so that it existed in multiple places at the same time.
An interesting detail about the Kin’s time-travel abilities was that, while it could move back and forth through time as it wished, it could only fully establish its temporal position by tricking other entities into asking it what the time was, allowing the Kin to create quantum superpositioning that would subsequently anchor to a place-time location (Presumably, until this was done, they would be unable to have any impact on their locations, much like the time-travelling restaurant the Crystal Bucephalus could control how strong an impact their guests had on the past when they were projected back in time (“The Crystal Bucephalus”).
Although the Time Lords naturally set out to stop the Kin due to the danger they poses to the Web of Time, they didn’t kill any of the Kin as the Kin’s nature as a single entity at different points in time meant that killing any would be genocide, and thus contravene the Time Lords’ rule of Article Seven (The Trial of the Timelord story “Terror of the Vervoids”). They thus imprisoned the Kin in a prison out of temporal phase with the rest of the Universe, centuries in Gallifrey’s past; even The Doctor had only heard the story of the Kin as a small boy on Gallifrey, before he went to the academy. The true face of the Kin was perceived by Amy Pond when it removed its mask to scare her as a ‘crawling, squirming, wriggling mess’.
After the Last Great Time War, the Kin was able to escape its prison, the alerts set up to warn Gallifrey of its escape naturally useless now that there was no Gallifrey to alert (“The End of the World” and “The Day of the Doctor”). Wanting to lure in the last of the Time Lords to complete its domination, the Kin travelled to Earth 1984 and began to legally buy the planet using money recycled through time. The Kin wore a variety of masks while on Earth to cover up its face – it was unspecified where these masks came from, but evidence suggests that it originally purchased the masks from other humans before gaining the ability to create its own, more convincing disguises – including a rabbit mask, Margaret Thatcher, and Amy Pond. As a result of its actions, by 2010 it had created an alternate timeline where humanity was extinct and Earth was legally its property, alerting the Eleventh Doctor and Amy to their activities when they tried to return to Amy’s time, prompting them to travel back to 1984 to investigate, arriving in the village where the Kin had started its campaign. When The Doctor identified their enemy after the Kin killed a young girl called Polly whose house it had recently purchased when she discovered its true nature while trying to find her diary, the Kin disguised itself as Amy so it could access the TARDIS, and told The Doctor to go to the Dawn of Time, ‘Amy’ arguing that it was the best location to retreat to in order to escape the Kin.
Revealing its identity after The Doctor had set the TARDIS in motion, the Kin revealed its plan; it would gain control of all time by stepping outside of the TARDIS at the moment of the Big Bang so that it could infuse all matter in the universe with the essence of the Kin. However The Doctor, having realised who the Kin was as the TARDIS was set in motion, had travelled to a point before the Big Bang (Most likely some moment between the end of the previous universe and the beginning of this one, considering the existence of the Great Old Ones such as the Animus (“The Web Planet”) and Fenric (“The Curse of Fenric”) as entities from the universe that existed before ours), informing the Kin that he would have helped it find another way if it had not killed Polly. As a result, when the Kin stepped out of the TARDIS it was trapped before time, negating all of its actions on the universe, resulting in The Doctor returning to 1984 to find Amy drinking tea with Polly’s family and Polly still alive.