What is up with the angel statues on Doctor Who?

Answer 1

They are an alien creature called Weeping Angels.

They have an amazing defence against harm, and that is they become 'stasis locked' when anything looks at them. They just appear to be stone statues then. But while unobserved, they are capable of moving very quickly, able to pounce on someone in the time their eyes are closed as they blink.

They do not kill people directly, they feed by sending people back in time. This creates a form of temporal energy that they absorb. They can also absorb other energy sources too, one use is to kill the lighting in a room so they can't be seen.

Their strength can also be a weakness though. If two ever catch sight of each other, both would be permanantly stasis locked until something else obscured their vision. This is why they are referred to as the 'lonliest beings in the universe' and a reason why they are shown covering their eyes, giving the appearance of mourning.