The Alliance was an association of diverse races, including many of the Doctor's enemies, formed to stop the greatest threat in the universe, which they all believed to be the Doctor. They predicted that the explosion of his TARDIS would cause the cracks in time, which in turn would end all of existence.
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The Alliance devised a plan to trap the Doctor in a specially-built prison known as the Pandorica to prevent him from piloting his TARDIS. However, none of them knew River Song could pilot the TARDIS as well, which led to the explosion. They were temporarily removed from existence, but thanks to their creation, the Pandorica, the Doctor reversed the damage done by the silence and restored them to their proper times without memory of their alliance.
History
Members of the Alliance visited Amy Pond's house the night she left with the Eleventh Doctor in 2010. They traced the psychic imprints there, sampled Amy's memories and used them to create a scenario the Doctor could not resist to lure him to the Pandorica. This resulted in the Nestene Consciousness creating Autons disguised as a small legion of Roman soldiers from a picture book that Amy owned. They were set near Stonehenge, also featured in the picture book, in the year 102 AD. Among the Auton duplicates was a copy of Rory Williams, presumably created because a photograph of Rory in a Roman centurion costume was kept in the pages of the book. The Pandorica, named for "Pandora's Box", another book Amy owned, was placed under Stonehenge. A Cyberman was placed with the Pandorica to act as a sentry, but ended up getting damaged by the locals and losing his head and getting destroyed later by Auton Rory to save Amy and the Doctor from it.
Stonehenge acted as a transmitter, summoning members of the Alliance to converge on the Pandorica when the Doctor arrived. The Doctor managed to keep them at bay for an hour by extending the Pandorica's force-field technology around Stonehenge; he also warned them to "do the smart thing" by letting someone else try first due to how many times he's defeated them in the past. Once the Pandorica was ready to open and hold the Doctor indefinitely, a high-pitch signal went out to the Auton copies and activated their programming; however, Rory's copy possessed the heart and soul of the original, allowing him to fight back.
They confronted the Doctor and explained their intentions. They had concluded that the cracks would be caused by the destruction of his TARDIS; therefore they sealed the Doctor inside the Pandorica to prevent him from using it, believing only he could pilot the TARDIS and this would avert the disaster. As they sealed him inside, the Doctor tried to save them and the entire universe, warning them desperately of the true threat. However, unknown to them, River Song, the Doctor's wife and companion, could also pilot the TARDIS. She was attempting to do so at that time, which caused the destruction of the universe. The Alliance's plan failed and all the Alliance species, including the Daleks, Cybermen, Judoon, Sontarans, indeed, everything in the entire Universe save the Earth and Moon, were wiped from existence, leaving only stone 'after-images' behind. The stars, including the Sun, no longer existed, because they all went supernova at the same moment. According to the Cybermen, all of the alternate Universes and the Void were also wiped from existence. (TV: The Pandorica Opens)
The Doctor piloted the Pandorica into the TARDIS explosion, creating a second Big Bang that "reset" the universe. This removed the cracks from existence. Technically, due to the Pandorica being used to save the universe, the Alliance helped the Doctor in the effort, so their plan did succeed. The cracks never existed and the Alliance was never formed[disputed statement]. The members of the Alliance were restored to their original forms and places in space and time. (TV: The Big Bang)