Magnetism is actually a range of phenomena. Magnetic fields are produced by currents and moving charges. They can also be produced (or cancelled) by certain materials, but the magnetic field produced is actually a side effect of the aligning to some extent of the magnetic fields produced by the electrons as they orbit the nuclei.
Magnetic materials fall into three categories.
Diamagnetic
If a sample of diamagnetic material is placed inside a magnetic field, a field is produced inside the material that opposes the external field. The magnetic fields produced by the electrons orbiting the atoms cancels the external field.
Paramagnetic
Paramagnetic materials are closer to what we think of as 'magnetic'. If a paramagnetic material is placed inside a magnetic field, the magnetic fields produced by the electrons as they orbit the nucleus tends to be aligned with the external field. The degree of paramagnetism is reduced with increasing temperature because increased vibration of the atoms tends to disturb the orbits of the electrons and the associated magnetic fields.
Ferromagnetic
The atoms in ferromagnetic materials align with neighbouring atoms to form a grain like structure insie the material. There are only a few ferromagnetic materials made of single elements– iron, nickel, cobalt, gadolinium and dysprosium but there are more ferromagnetic alloys. If ferromagnetic materials are heated enough, the grain structure breaks down before the material actually melts and the material becomes paramagnetic. Ferromagnetic materials may be used to make permanent magnets. When the external field is removed a magnetic field is still present because of the field produced by the magnet.