Most designs are naturally stable across their entire performance envelope, allowing the aircraft to be flown without the pilot needing to constantly correct the flight path. This also implies a loss of manuverability, the more stable the plane is the more it wants to continue flying as it is, and the more effort has to be applied to manuver it.
Stability increases as speed increases, a side effect of the higher airflow over the control surfaces. This presents a design problem for planes that need to be manuverable at high speeds, like fighter aircraft, because then at lower speeds the decreased stability may make them difficult to control. Since takeoffs and landings occur at low speeds, this is usually the limiting factor -- planes are thus designed to be just stable enough to fly at low speed, and the high speed manuverability is whatever it gets.
The introduction of automatic flight controls and fly-by-wire systems changed this equasion considerably. Now the low speed control was no longer an issue, any inherent "drift" off the flight path not commanded by the pilot can be detected and automatically corrected for. This gives the plane an artificial stability to make it flyable at any speed. Meanwhile this lowered stability means the plane remains manuverable at higher speeds.
Although such systems had been in use for many years in military aircraft, notably for yaw damping, the first truely relaxed stability fighter was the F-16 Fighting Falcon. Using an advanced (for the time) flight control system allowed the plane to fly very "flat" to the air as well, increasing performance and range. It was able to completely outperform the F-17 Cobra in head-to-head competition, and went on to become one of the most produced post-war US designs. Today almost all fighter designs make extensive use of relaxed stability and automatic flight controls, and watching the rapid movement of their control surfaces as they land will demonstrate how unstable these designs are.
Relaxed stability has since moved into the civilian market as well, although for other reasons. Today most modern airliners use a fly-by-wire system in order to save weight, but a side effect of this is that the planes can use relaxed stability to fly flatter and thus save fuel. First introduced on the Airbus A320, today almost all large airliners use some sort of relaxed stability in their designs for this reason.