Let us breakdown this title into stability and aircraft stability. We will have a glimpse on what the meaning of stability is and apply it to the aircraft. Stability is the ability to return into equilibrium state after an excitation is applied to an object.
In aviation the concept of stability is divided into two parts in which one of them helps the other. The first is the static stable aircraft where an aircraft has the tendency to return to its normal condition if for example air turbulence disturbed its condition, it would be able to return to its level flight, heading, or to be able to maintain its speed. To have a positive static stability all forces and moments acting on the center of gravity must be equal to zero.
The second type is dynamic stability. In dynamic stability analysis, the concern is on the response to control surfaces (ailerons, elevators, or rudder), and atmospheric inputs of aircraft with the respect of time. The relationship between the static and dynamic stabilities is to have a dynamic and stable aircraft so that the aircraft must be static stable.
There are many parameters must be taken inconsideration to determine the stability of the aircraft. Some can be on aircraft length, center of gravity, and wingspan. Thus, the aerodynamicist are working hard before the real build of an aircraft on calculations and equations of stability to come up with the goal of either maneuverability or high stability. For example, a jet fighter is highly maneuverable and low in stability on the other hand the commercial aircraft is highly stable in which to change direction it takes some time.
For engineers this is not the end of the stability topic because there is the control topic. Moreover flight level quality are compulsory to help the engineers determine how complex the control system will be.