A magnetic field line is that path in space that points in the direction of the magnetic field at every point along it. Walk along a magnetic field line carrying a compass, and the needle will always point in the direction you need to go in order to stay on that magnetic field line (the needle has to be able to pivot up and down as well as around in a circle like most compasses).
If two field lines crossed, then that is resembling that the magnetic field points in two different directions, at one place. There is only one direction to the magnetic field at any place at any time, so this doesn't happen.