Big Bang Two

The Big Bang Two referred to the explosion caused by the Eleventh Doctor, "rebooting" the universe after its destruction.

A day to come
Through the extrapolations of the Matrix, the Time War-era Time Lords foresaw this event from the Doctor's personal future, which was recorded in the Dalek Combat Training Manual. The Time Lords observed that the universal reboot caused subtle changes to the timeline of Earth, resulting in the events such as 21st century Dalek invasion being forgotten, explaining how humanity at large was unfamiliar with the Daleks during the 2021 Dalek civil war. (PROSE: Dalek Combat Training Manual)

The Bang
At "every point in history, all suns in the universe had gone supernova" due to the unique circumstances of the TARDIS' destruction on 26 June, 2010. The entire universe was destroyed and erased from existence except for the Earth and its Moon. The TARDIS' continuing explosion throughout all of history, putting itself in a time loop at the moment of its own destruction, acted as a replacement for the Sun, keeping humanity alive.

When the Pandorica was opened in 1996, it contained billions of atoms from the universe as it should have been. Some of these were the final traces of whole races erased by the cracks in the universe. As "the perfect prison", the Pandorica was also designed to emit a restoration field to preserve or restore whatever was inside it, preventing prisoners from escaping even by dying. This combination of pre-collapse atoms and the restoration field had a restorative effect on a fossilised Dalek. This seemed impossible, because the Daleks had never existed, having been erased from history; there should have been nothing to resurrect. The Eleventh Doctor thus reasoned that if the restoration field could be transmitted throughout all of space and time, the entirety of the former universe could be extrapolated from the atoms within the Pandorica.

The Doctor used a vortex manipulator to fly the Pandorica directly into the heart of the TARDIS' eternal explosion. Since the TARDIS was exploding at all points in history, the particles and restoration field were present at every point in time. A new universe was created based on the old one, but with the Doctor having never existed, as he had to 'seal' himself outside the universe in order to close the cracks. "Rebooting" the universe caused this new universe to proceed undamaged, because the TARDIS had not exploded. Thanks to the ability the crack in her room had given her to restore things erased by remembering them, on 26 June, 2010, Amy Pond brought back, at least her parents and fiancé Rory, and at Rory's and her wedding, the Doctor after she focused on remembering him. (TV: The Big Bang)

Behind the scenes

 * Because this new universe's creation depended on certain erasures when compared to the history of the original universe, it is unknown whether any particular previous Doctor Who adventures ever took place. However, it is assumed they did once Amy brought the Doctor back, as the content of River Song's diary were replaced. Also, in A Good Man Goes to War, the Thin One and the Fat One confirm that the Atraxi's thwarted attack on Earth and the Doctor's subsequent telling off still happened in the rebooted universe. In the fourth series of The Sarah Jane Adventures, set after these events and featuring the Eleventh Doctor, confirms that all the events prior to the Big Bang had still happened in the rebooted universe.