Arbiter's Grounds is a location from The Legend of Zelda: Breath of the Wild. The area is located in the Gerudo Desert region of Hyrule. The area is mostly barren aside from the destroyed pillars and the main entrance. Several Lizalfos can be found in the area. Molduga also infest the area and attack Link if he gets too close. A Korok Seed can be obtained from a hidden Korok found atop one of the pillars.
Given its name and ruined state, it is implied to be the ruins of the Arbiter's Grounds from The Legend of Zelda: Twilight Princess. It may indeed be the ruins of the old prison consumed by the desert sands and eroded by both sandstorms and desert winds. Alternatively the Gerudo destroyed it upon reclaiming their ancestral home due to the prison reminding them of their ancient king Ganondorf leaving behind only ruins. Alternatively Ganon or his followers destroyed it some point after Twilight Princess. It should be noted the Kingdom of Hyrule all but abandoned the prison following Ganondorf's failed execution and Gerudo Desert becoming inaccessible by land which likely contributed to its decline and ruined state by the time of Breath of the Wild. The local Molduga tunneling under the sand could also contributed by damaging the old prison grounds' foundation possibly under Ganon's influence or command.
Former Desert Colossus
If it is the former Arbiter's Grounds prison and the prison was the Spirit Temple converted into a prison, then the area around it is likely the former Desert Colossus area which is supported by the fact a Great Fairy Fountain and the Southern Oasis are located near the Arbiter's Grounds in Breath of the Wild like the Desert Colossus area in Ocarina of Time which had an oasis (dried up unless filled by rain) and a hidden Great Fairy Fountain. Of course it could also simply be a reference to the Desert Colossus' layout similar to Ranch Ruins sharing Lon Lon Ranch's layout from Ocarina of Time.