Interaction of rotor magnetic field and stator magnetic field generates a force, which creates torque for the rotor to rotate.

During rotation since the orientation of current flow direction relative to stator reverses hence the direction of induced force and rotation remains the same.

During rotation since the orientation of current flow direction relative to stator remains the same as before the direction of induced force and rotation stays the same.

During rotation when commutator comes in contact with a brush, the direction of current flow reverses in those rotor coils however this creates the correct configuration for rotation continuation.

During rotation when commutator comes in contact with a brush, the direction of current flow remains the same and hence the rotation continues.