They take on the form of stone statues when they are being watched by any creature, and can move when no creature is looking at them.

Because they are a creature themselves, they are not crying, but only pretending to cry, in order to cover their eyes and avoid looking at each other. For once they looked at each other, they would remain in a state of stone and never be able to move again.

The ending of Season 3, Episode 10, is when the Doctor removes the Tardis while the four angels are hugging it from all sides, causing the four angels to look at each other two by two, turning them into true stone statues.