The Dalek Asylum was a snowy and mountainous planet used by the Daleks as a prison and "dumping ground" for those among them who had malfunctioned, gone insane and/or become mentally scarred by battles. The Dalek Asylum was protected by a force field and a nanocloud, which converted beings that did manage to enter into Dalek puppets. The sane Daleks left their insane fellows in the Asylum rather than kill them because they epitomised the Dalek concept of beauty: pure hatred. Even the Daleks don't know how many of their brethren are incarcerated on the planet, but tell the Doctor through Darla that its in the millions at least.
Even amongst the deranged Daleks, there was still an area described as "intensive care", which housed several Daleks who had survived conflicts with the Doctor on planets such as Spiridon, Kembel, Aridius, Vulcan, and Exxilon. (TV: Asylum of the Daleks)
The Alaska was able to breach the Dalek Asylum's force field and crashed into the planet. Junior Entertainment Manager Oswin Oswald was fully converted into a Dalek by the inmates, while the rest of the crew were converted into Dalek puppets by the Asylum's nanocloud. The Asylum was originally fully automated, but over the course of a year, Oswin was able to reduce the Asylum to a ruin by hacking into its systems.
A year after the Alaska crashed on the Asylum planet, the Parliament of the Daleks feared the insane Dalek inmates could escape. In order to destroy the planet and the Daleks inhabiting it, they kidnapped the Eleventh Doctor, Amy Pond, and Rory Williams, and sent them to the surface (by way of a gravity beam) in order to deactivate the planet's defences, as no Dalek was willing to infiltrate the Asylum themselves due to fear of the insane Daleks.
On the planet, the Doctor, Amy and Rory were guided by Oswin who was unaware of her status as a Dalek. Due to her hacking, Oswin could lower the Asylum's force field, but refused to do so until the Doctor rescued her from the escape pod she believed she was trapped in. The Doctor eventually reached the intensive care unit where the Daleks, who were normally completely catatonic, woke up in his presence due to their hatred of him. Before the Daleks could kill him, Oswin hacked the Dalek Pathweb and erased all memory of the Doctor from the Daleks to his shock as even he couldn't hack the Pathweb. Moments later, he learned of Oswin's conversion after finally finding her and she nearly gave into her programing in her despair over the situation. Breaking down, Oswin regained control and decided to end her own existence and that of the Daleks. Oswin lowered the Asylum's force field and ordered the Doctor to run and remember her. As the Dalek fleet fired on the defenceless Asylum, the Doctor was able to use a teleporter to teleport himself, Amy and Rory aboard the TARDIS on the Dalek ship in orbit. Once the Asylum defences were down, the Daleks fired missiles at the planet, blowing it up and killing the Daleks trapped there. To the Doctor's surprise, when he emerges from the TARDIS to taunt the Daleks after they detect his teleport, Oswin erased the knowledge of his existence from all the Daleks in existence, not just those on the Asylum. (TV: Asylum of the Daleks)
When the Great Intelligence invaded the Doctor's time stream on Trenzalore to turn all of his victories into defeats, the Dalek Asylum was one of the many places where the Doctor died. When Clara Oswald followed him into the time stream, it was revealed that "Oswin Oswald" was one of many versions of Clara scattered across the Doctor's history with the purpose of saving his life. (TV: The Name of the Doctor)