full text of the classic FAA guide
STABLE AND UNSTABLE AIR
To a pilot, the stability of his aircraft is a vital concern. A stable aircraft, when disturbed from straight and level flight, returns by itself to a steady balanced flight. An unstable aircraft, when disturbed, continues to move away from a normal flight attitude.
So it is with the atmosphere. A stable atmosphere resists any upward or downward displacement. An unstable atmosphere allows an upward or downward disturbance to grow into a vertical or convective current.
This chapter first examines fundamental changes in upward and downward moving air and then relates stable and unstable air to clouds, weather, and flying.