Neutral point and static margin come in the context of longitudinal static stability.

Neutral point :

If the position center of gravity is allowed to move, with other things fixed like position of the aerodynamic center, then there will be a position of center of gravity where change in the coefficient of moment about this center of gravity with respect to the absolute angle of attack will be zero, that is\( \frac{{\partial {C_{M,cg}}}}{{\partial {\alpha _a}}} = 0\). There will be also positions of center of gravity when this will be negative or positive. When \(\frac{{\partial {C_{M,cg}}}}{{\partial {\alpha _a}}} = 0\), the position of center of gravity at this point is called neutral point. Neutral point is a fixed point on the aircraft. Center of gravity can move forward and aft of the neutral point. When the center of gravity is forward of the neutral point the aircraft has longitudinal static stability. If it is on the neutral point, it has neutral longitudinal stability, and if it is aft the neutral point it has longitudinal unstability.

Static margin :

It is the distance between the center of gravity and the neutral point of the aircraft, which is expressed with respect to the mean aerodynamic chord of the wing. For longitudinal static stability aircraft’s center of gravity must be forward of the neutral point, that is static margin should be positive. The larger the static margin, the more stable will be the airplane. Therefore, to make an aircraft more responsive to pilot inputs static margin is reduced, that is there will be a low static margin, for such airplanes.

Neutral point, center of gravity and static margin of an aircraft