This also acts as a defense mechanism as while they are turned to stone they can not be killed however they can not kill either. The Angels can move at incredibly fast speed being fast enough to move across a street in the Blink of a eye this helps dramatically to stalk their prey.
The angels are according to the Doctor as old as the universe or very nearly and no one really knows where they come from. The Doctor describes these as "creatures of the abstract", "the lonely assassins", and "the only psychopaths in the universe to kill you nicely" because of their method of killing. All they need to do is touch a victim and this sends their victims into the past to live out their lives before they were even born. The Angels then feed on the potential energy of the lives their victims would have lived in the present.