What the video calls the neutral plane (I call it the geometric neutral plane) contains the motor's axis of rotation and is perpendicular to lines of field flux when no armature current is flowing.
Armature reaction (caused by the magnetic field that arises from armature current) tends to rotate field lines against the direction of motor rotation. The video terms this rotated neutral plane the adjusted neutral plane. I call it the electrical neutral plane.
When an armature conductor passes through the electrical neutral plane, it's moving parallel to magnetic lines of force, and hence no back EMF is induced as a result of the conductor's motion. However, some additional back EMF is self-induced as armature current decreases (caused by armature inductance). These two phenomena work together to rotate the electrical neutral plane in the same direction.
When voltage in an armature conductor is zero (that is, when it passes through the electrical neutral plane), this is the ideal point at which to commutate the current.