An applied MMF 'drives' magnetic flux through the magnetic components of the system. The magnetic flux through a magnetic component is proportional to the number of magnetic field lines that pass through the cross sectional area of that component. This is the "net" number, i.e. the number passing through in one direction, minus the number passing through in the other direction. The direction of the magnetic field vector B is by definition from the south to the north pole of a magnet inside the magnet; outside the field lines go from north to south.