In re-orienting the the iron filings, the magnet is applying a force. The new orientation of the iron filings shows the direction of the magnetic field around the magnet.

Rather than sprinkle iron filings around magnets of interest, scientists draw magnetic fields using magnetic field lines (more strictly known as magnetic lines of induction), to show which direction the magnetic field is pointing. The field lines are drawn along the direction of the magnetic field and along the direction the iron filings would point. In fact, although only a few lines are usually drawn, the magnetic field exists between the lines too. The intensity of the magnetic field is represented by the spacing of the magnetic field lines; a strong magnetic field has the lines close together. Compare the field lines for the magnet below to the iron filings experiment.