The most important thing to understand about attractors is that they are islands of stability in a sea of chaos.
Dynamic complex systems are inherently chaotic and unstable, but, they usually settle down into one of a number of possible steady states. These steady states are called "attractor basins". It is by causing dynamic complex systems to switch between attractor basins that control can be exercised. The following article is a good starting point for learning more about this essential subject area.
Attractors Everywhere - Order from Chaos by Chris Lucas