(covers information from several alternate timelines)
Hundreds of years prior to the 22nd century, a set of katric arks was discovered at the P'Jem monastery. The arks were scanned and analyzed, and one of the scientists even attempted to initiate a mind meld with them, all to no effect.
In 2137, Syrran, leader of a Vulcan dissident movement, discovered the ark containing Surak's katra on Vulcan. Syrran was successful in transferring Surak's katra to his own mind, successfully carrying it until his death in 2154, at which time he transferred the katra to Jonathan Archer, a Starfleet captain. (ENT: "The Forge", "Awakening")
In the alternate reality created by Nero's temporal incursion of 2233, the katric ark was also the name of a large facility on Vulcan used for the preservation of Vulcan heritage and culture. The ark was impenetrable to both communications and transporter signals.
In 2258, as Vulcan was on the verge of destruction due to an attack by Nero, the Vulcan High Council, including Sarek and his wife Amanda, retreated into the ark in an effort to save the knowledge contained within. As this was occurring, Sarek and Amanda's son, Spock, arrived to evacuate the High Council. Spock and the Council emerged from the ark on a cliff and awaited transport by the USS Enterprise, although Amanda was killed when the cliff gave way beneath her due to heavy seismic activity. (Star Trek)
Roberto Orci, a co-writer and producer of the film Star Trek, confirmed a fan's suspicions that what the Vulcan elders in the katric ark in that film were doing was retrieving the katra of Surak and possibly the katras of other Vulcans – so that Sarek became the carrier of Surak's katra – and that the writers at least considered having one of the other elders carry the Kir'Shara from the katric ark. 
As demonstrated in a concept painting, the interior of the film's katric arc was originally planned to have a series of triangular stairways and a pillar of spiraling particles (either water or energy) floating in midair. According to Industrial Light & Magic art director Alex Jaeger, the idea of the fantastical pillar was discarded by producer/director J.J. Abrams as he deemed it to be "too sci-fi magical." A concept painting of the corridor leading to and from the katric ark was illustrated to look more spacious than how it appears in the film, with walls that seem more man-made than the ones in the movie. More successful was concept art showing the katric ark's cliff-side portal, which looks more-or-less identical to the one shown on-screen. (Star Trek - The Art of the Film, pp. 110 & 111)
ILM was involved in creating an establishing shot of the enormous statues inside the katric ark. (audio commentary, Star Trek Special Edition/Three-disc Blu-ray) Roger Guyett, the film's visual effects supervisor and second unit director, explained, "The temple was pretty much just a floor on a big greenscreen stage. ILM added all the walls and statues as digital set extensions." (Cinefex, No. 118, p. 59)
In several Star Trek novels, such as The Lost Years, the katric ark facility is a chamber within Mount Seleya known as the "Hall of Ancient Thought". In the Hall are thousands of receptacles (vre'katra) containing the katras of the greatest and most powerful Vulcan masters throughout history. Vulcan scholars, philosophers, and mystics could petition to be permitted to meld with these katras for research or enlightenment.