Normal force
A normal force FN is a force, [1] a contact force's component perpendicular to the surface (contact plane; POC) an object touches. [2] FN is a pushing force, not pull, which is rather the gravity or weight force (FW).
[3] If a weight sits on a POC, it exerts a downward weight (pull) force, the graviational pull, that pulls the weight to the Earth. The POC itself exerts an upward force, its normal force, thus the weight is in an equilibrium state, i.e., the gravitational pull is cancelled by an equal upward force and perpendicular to the POC. If a weight sits on an inclined plane, its FN is also perpendicular to the plane it's on. Increasing the weight's downward force (FA) increases the FN, as the surface must exert an upward force to support the object's weight and downward applied force we applied.
To decrease the weight's FN, we must apply an upward force on it, e.g., we must lift the object. E.g., Via a rope attached to it, we can apply a tension force (T) which reduces the stress on the POC.
While, not the same as A FN, normal force due to weight (FNw) is the normal force's portion/support force needed to counteract gravity/FNw.
[3] FN can be negative if the object is no longer in contact to a POC, thus the net force in y-axis isn't 0 with an acceleration instead. If a FN exceeds the FW, the object moves up and FN vanishes. This is demonstrated in E.g., 1.3.
