Quantum-locking was a defence mechanism used by the Weeping Angels. When observed by any living creature (even other Weeping Angels), the Weeping Angels turned to stone, making them resistant to harm. When they weren't being observed, the Weeping Angels could move. Weeping Angels could also turn to stone at will, or when they believed they were being observed. (TV: Flesh and Stone) However, if the Weeping Angels stared at each other (TV: Blink) or at a reflection of themselves (TV: The Time of the Doctor, PROSE: The Mirrored Room) they would turn to stone permanently, leaving them trapped until they died from starvation.
Others species were also capable of quantum-locking. The Medusa used it to leave people frozen in time, in order to feed on their life energy. (COMIC: Gaze of the Medusa) Furthermore, the Mouri in the Temple of Atropos were said to have been quantum locked, and only appeared once someone was in close proximity to them. The temple was also redesigned so as to prevent the seal from recognising Swarm and Azure, thereby preventing the Mouri from appearing when they alone were near. (TV: War of the Sontarans)
Behind the scenes
The quantum-locking mechanism is similar to the so-called quantum Zeno effect, a situation in quantum mechanics in which an unstable particle, if "observed" continuously, will never decay forming another particle. For example, the observation can "freeze" an unstable atomic nucleus, preventing the emission of particles or radiation. In other words, a uranium atom can decay only when not being measured or interacted with.
In the webcast Stealing Series 9 Scripts, the in-universe counterpart of Christel Dee is able to use a sonic screwdriver to quantum-lock a lava pool which served as one of the defence systems on Steven Moffat's "secret writing lair" below 221B Baker Street. However, the webcast is not considered a valid source on this Wiki due to its somewhat parodical nature and its free-form blending of in- and out-of-universe elements.