The Reapers are creatures that exist outside of time. When time is wounded, and a paradox caused, the Reapers sterilize the wound by consuming everything inside it. There is a suggestion that the Reapers are less of a timeline repair system and more of a parasite; any disturbance in time makes them stronger, and the Doctor refers to them as "taking advantage" of the wound in time, like bacteria. This kind of uncontrolled activity by the Reapers used to be prevented by the laws of time, but with the Time War and the destruction of Gallifrey, such laws seem no longer to apply, much less be enforced.
Physically, the Reapers resemble dragons. They have a spade-shaped head with bright red eyes (meaning they see everything through a red filter), four arms arranged around a toothy mouth in the center of their body, two broad three-fingered wings, and a sickle-shaped tail. When Reapers feed, their heads and necks emit a yellow glow. They can remain invisible, although it is unknown what exactly prompts them to reveal themselves and hunt in the open. The noise they make is a cross between crowing and cackling.
Basically, the Reapers are unstoppable. Once they have found a wound in time, they attack everyone present, causing them to vanish completely from the timestream. Older things are able to withstand the Reapers longer, but cannot hold them back forever. Along with a gradual disappearance of people, the Reapers cause apparent temporal paradoxes (future songs being played over the radio, or the first telephone message being transmitted over everyone's cell phones), a drop in temperature, and external dimensions like the TARDIS interior are cut off from the infected world. The only way to escape the Reapers, apparently, is to resolve the paradox that attracted them, after which they vanish.
