A restoration field was a device that could restore people and objects to their natural state.
A restoration field was added to the Pandorica so the Eleventh Doctor would be unable to escape by dying. It was used by the Doctor, once he escaped, to reanimate the nearly dead Amy Pond; to restore a near dead living being it needed a sample of the living being's DNA. In Amy's case, this came from her younger self.
It later reanimated a Stone Dalek. The Doctor used it to revive himself when the Dalek shot him, nearly killing him. It is unknown where the Doctor got the DNA to heal himself, though since the Pandorica was already open, it is possible he did not need it.
River Song said that a restoration field could not restore the universe on its own. Whether she meant it did not have enough power to do it on its own, or whether it had to be used in conjunction with the cause of the destruction is unknown.
With the universe destroyed, the Doctor planned to use the restoration field to "reboot" the universe. By flying the Pandorica into the heart of the TARDIS's explosion, the light was spread throughout the universe at every point in time, rebooting the universe and also negating the total event collapse. (TV: The Big Bang)