Stall occurs when a plane is under too great an angle of attack (the angle of attack is the angle between the plane and the direction of flight). It may occur during take-off or landing, when the flight speed is relatively low: at low speed the aerodynamic forces are correspondingly smaller, and the only way to get enough lift to carry the weight of the plane is to fly the plane at a greater angle of attack. If an inattentive pilot lets the speed get too low, the plane will exceed the critical angle of attack and stall occurs.
Due to the stall the wing produces less lift and more drag; the increased drag causes the speed to decrease further so that the wing produces even less lift. In effect, the plane falls out of the air. The ground waits below.
Below is a numerical simulation in which a stalling wing is seen in cross section. The leading edge is left, the trailing edge is right. In the simulation, the boundary layer is represented as vortices (miniature tornados) which are displayed as black or white dots, depending on the direction of rotation. The wing pitches up to an angle of attack of 30 degrees, causing the stall:
t = 1 (starts pitching)
In the first picture the wing is moving at a small angle of attack (here taken as zero). Note that the boundary layer vortices remain close to the wing until they are washed downstream. At zero angle of attack, there is no lift, and there is little drag.
t = 2
t = 3
The wing has started pitching up, but the boundary layer vortices stay close to the wing. The wing is now producing significant lift force, and still little drag.
t = 3.5
t = 4.25
t = 5 (ends pitching)
The angle of attack has become too large. The boundary layer vortices have separated from the top surface of the wing, and the incoming flow does no longer bend completely around the leading edge. The wing is stalled, causing a significant drag. However, much of the lift remains since the separated vortices are still above the wing.
t = 6
When the separated vortices are being blown past the trailing edge, the lift starts to drop off.
t = 7
The wing is now producing little lift, and lots of drag. However, it is easier for air to flow around a leading edge of a wing without lift, and the flow starts to reattach.
t = 7.5
t = 7.75
t = 8
The flow has largely reattached, and the lift coefficient (the lifting efficiency of the wing) is temporarily restored. Unfortunately, this will set up a new cycle of separation; further, the increased drag reduces the airspeed too much to produce much lift, even at a good lift coefficient.
t = 8.5
t = 8.75
t = 9
Here are the evolution of the lift, drag and moment coefficients:
The plane starts picking up speed, going down even faster. But as soon as the plane has picked up enough speed so that the wing can again support the weight of the plane, the pilot pulls back on the stick to increase the angle of attack again (this time staying in the allowable range), and restores the lift of the wing.
Obviously, to recover from a stall involves some loss of height. Stalls are most dangerous at low altitudes. Engine power can help reduce the loss of height, by increasing the velocity more quickly and also by helping to reattach the flow over the wing.
How difficult it is to recover from a stall depends on the plane. Some planes that are difficult to recover have stick shakers: the shaking stick alerts the pilot that a stall is imminent. The stall characteristics also depend on how a plane is loaded; the center of gravity of the plane must be sufficiently far foward.
The mechanics of a spin are complex. Depending on the plane, (and on the way it is loaded!) it may be more difficult or impossible to recover from a spin. Recovery requires good efficiency from the tail surfaces of the plane; typically recovery involves the use of the rudder to stop the spinning motion, in addition to the elevator to break the stall. However the wings might block the airflow to the tail. If the center of gravity of the plane is too far back, it tends to make recovery more difficult. The pilot can get disoriented by the dizzying effects of the spin, and apply the wrong corrections.
Even if the plane is well designed, loaded within the allowable range and recovery is executed flawlessly, the height loss in a spin can be very large. Since stalls and spins are most likely during take-off and landing, there may simply not be that much height available. Under FAA rules for private pilots, stall training is required, but spin recovery is not. Stall training allows the pilot to recognize an impending stall, and take corrective measures before a true stall and maybe a spin can occur.
Shih, C., Lourenco, L., Van Dommelen, L. \& Krothapalli, A. (1992) Unsteady flow past an airfoil pitching at a constant rate. AIAA Journal 30 1153-1161.