The Pandorica was a prison box, hidden under Stonehenge. It was constructed to ensure the safety of the Alliance and to hold the most feared organism in the history of the Universe, which turned out to be the Doctor. It was mentioned by Prisoner Zero to the Doctor, who told him that it would open and that silence would fall. (DW: The Eleventh Hour) River Song also mentioned the Pandorica to the Doctor, telling him she would next see him there and that she remembered it well. The Doctor believed at that time that the Pandorica was a fairytale. (DW: Flesh and Stone)
The Pandorica turned out to be a prison, built by the Alliance for the Doctor to stop him from destroying all the universes. Their conclusions held that the Doctor would be responsible for the destruction of existence itself and thus used the lure of the Pandorica in order to entrap him. There were many layers of security in the Pandorica including deadlocks, time stops and matter lines. (DW: The Pandorica Opens)
The Pandorica was also used by the Doctor to restore the universe. Since all of the traps inside it provided the perfect barrier against the destruction of the universe, it provided a literal 'blueprint' for the universe when the Doctor threw it into the exploding TARDIS which cracked all of time and space. The blueprint from the Pandorica combined with the explosion energy from the TARDIS restoring every point in time and the rest of the universe. Doing so also reset the timeline so the cracks never existed and all that was erased by them was restored. (DW: The Big Bang)
Appearence
Exterior
The Pandorica looked much like an image of Pandora's Box found in the bedroom of Amy Pond. Since they used her memories to lure the Doctor there, the Alliance possibly designed it to look like this.
Interior
The interior was a small room with a chair in it, intending to be a prison. When someone was placed on the chair, the exterior would close, sealing them in, and many forms of security would stop the prisoner escaping.
Known Prisoners
The Doctor was put in the chair by the Alliance to stop him from destroying every universe. (DW: The Pandorica Opens)
Though not a prisoner, Amy Pond was kept in the Pandorica by the Doctor and the Auton duplicate of Rory, after being killed. The imprisonment was meant to bring her back to life and she was restored when her seven year old self touched the box, causing it to open. Rory's duplicate guarded it from 102AD to 1996. One of the Pandorica's powers was to keep anyone from dying as that was a form of escape. Once it got a DNA sample from the young Amy, it was able to resurrect the older one. (DW: The Big Bang)