A common type of attractor, where the system's output constantly oscillates between two (or more) values. A fixed point occurs when the system moves toward a single output and stays there; by contrast, when the system's output moves toward a limit cycle, it will move from one point to another and back again, repeating the previous outputs in exactly the same way. The output is still changing, but at least it's stable and predictable.
Think of a solar system, for example. If a rock happened to be passing near a sun, and then crashed into it, the center of the sun would be the system's fixed point attractor. However, that's not the only possibility; a rock can also enter into an elliptical orbit, going around and around the sun in a regular and predictable way.
It was once thought that these two types of attractors were the only ones that existed, until the chaotic strange attractor was discovered. Like a limit cycle, an output near a strange attractor remains within a finite "space"; unlike a limit cycle, it does not consistently repeat itself.
See also attractor, fixed point, strange attractor