Magnetic materials form magnets in pairs of poles North and South. So a magnet always has N and S poles connected together physically.
North pole repels a unit North pole and attracts a unit South pole. Magnetic field line is the curved line in the plane of the magnet, which is traced by a unit north pole due to it magnetic force. If the unit North pole is moved very very slowly under equilibrium at each point, then the magnetic field lines are traced.
As North pole repels a unit North pole, the magnetic field line emanates from the North pole. Its direction is outwards from N. The unit north pole moves away from the magnet.
At the same time South Pole of the magnet attracts the unit North pole. So unit north pole moves towards S. So near the south pole, the magnetic lines move into the south pole, from all around it.
In between the North and South poles, the unit test north pole moves away from North pole and towards South pole in a smooth curve due to repulsion and attraction forces. The net force is always positive and never zero. Thus there is no break or null point in the curve.
The magnetic field lines give the direction of resultant magnetic field due to N and S poles of the magnet. Two magnetic field lines do not intersect as then it means that there are two directions for the magnetic field at that point. Since the resultant magnetic field is a vector, has a positive magnitude at all locations, South pole always attracts unit north pole , the lines end at South pole of the magnet.