Angel Bob was the name the Eleventh Doctor gave to the Weeping Angel from the vault of the Byzantium. He called this Angel by that name because it communicated by using a reanimated copy of cleric Bob's consciousness. Accepting this name for itself, it acted as the representative of its brethren when they fed on the power supply of the Byzantium.
Early history and the Byzantium
An army of Weeping Angels had wiped out the Aplan race on Alfava Metraxis in the mid-47th century, but in doing so had remained without a food source to feed on. They were trapped and weakened. Knowing of the fate of its brethren, a Weeping Angel lay patiently waiting in the ruins of Razbahan and feigned being in a "dormant" cycle. Just as it planned, it passed from one private hand to another until it came in possession of a temporal core to help revive its fellow Angels. The opportunity came when it came to be stored in the Byzantium.
River Song was sent by the Church to find and neutralise it. She got on board the Byzantium during her investigation and captured four seconds of footage of the Angel. Before leaving the ship, she warned Alistair it would not reach its final destination.
The Angel caused the Byzantium to crash on Alfava Metraxis above the Aplan Mortarium where the Angels remained, killing everyone on board. The once dormant and weak Angels within the catacombs beneath the temple began to awaken and regenerate.
On Alfava Metraxis
Father Octavian and a team of Clerics arrived at the crash site to track down the Angel. To explain what they were up against, Song showed the looped recording of the Angel to the Doctor, Octavian and Amy Pond. While the others left the pod, Amy remained with the recording in its constant loop. Unbeknownst to the expedition, any image of a Weeping Angel becomes itself a Weeping Angel. The image in the recording came to life and deadlocked the doors of the pod, trapping Amy within. The Angel projected itself beyond the image and into the room, until Amy was able to exploit a glitch in the recording to turn off the projection of the image. She had, however, stared into the eyes of the projection, opening her mind to it. (TV: The Time of Angels) This produced an image of an Angel in the visual centre of Amy's mind, opening her up to manipulation by the Angels, including hallucinations and death; as the image of the Angel within her would ultimately become a real Angel. (TV: Flesh and Stone)
The Angel escaped the vault of the Byzantium and went through the Maze of the Dead. When the Clerics Christian and Angelo were sent to investigate the further catacombs, the Angel killed them by breaking their necks. It took their central nervous systems and reanimated their consciousness temporarily to lure others to their deaths. It used the same procedure with the Cleric Bob on a more long-term basis, to communicate with the Doctor, Amy, River and the remaining Clerics.
The Angel continued to use Bob's remains to relay its messages to the Doctor, who began to call it "Angel Bob". It tried to anger him by having Bob tell him how his words of encouragement to the soldier had been lies. (TV: The Time of Angels) When the Doctor and the Clerics were surrounded near the Byzantium's oxygen factory, Bob said the Angels were amused at the Doctor not seeing the crack in time. Angel Bob informed the Doctor in the oxygen factory how the Angels' manipulation of Amy was just for fun, making him throw away his communication device in anger.
As the crack expanded, the Angels ran away and Angel Bob reappeared in person after the Doctor, River and Amy were cornered in the Byzantium's control room. He attempted to coerce the Doctor into throwing himself into the crack to seal it, saving the Angels and his friends. As the last of the ship's energy was waning, the Doctor forced a failure of the gravity field. Angel Bob and the other Weeping Angels fell into the crack, closing it and were erased from existence. (TV: Flesh and Stone)
Angel Bob showed no remorse at killing clerics and also claimed to enjoy doing it when it spoke to the Doctor using Cleric Bob's vocal chords and central nervous system. It tormented Amy with a copy of itself by making her think she was turning to stone.(conjecture) The Angel was very patient and clever; the Doctor guessed it had never been dormant but had allowed itself to be captured so it could get the needed power to revive its people.
It also possessed a sadistic sense of humour; it pretended at first to be Cleric Bob making his remains say what had happened to him. (TV: The Time of Angels) Later, after the copy of itself in Amy made her perform a countdown to the moment when the copy would consume her, Angel Bob indicated it was making her do the countdown for fun. (TV: Flesh and Stone)