Magnetic interaction can be observed in substances which are either ferromagnetic or paramagnetic. Ferromagnetic materials are made of many domains - regions where electrons have parallel spins. When magnetic field is applied, all of them arrange as if they form a crystal lattice, themselves.

Ferromagnetic materials are what we refer to by the term permanent magnet. Indeed, the strongest magnets are not made of either iron, cobalt or nickel, but from neodymium and other rare-earth metals. Its electron structure features 7 electrons with parallel spin within each atom. Thats a huge number. Atoms within a crystal stack up, so that all of their electrons are parallel.

Paramagnetic materials, on the other hand, dont have an ordered structure in the absence of a magnetic field. When it is applied, though, their electrons align, so that the spin of all their atoms are parallel. You obtain essentially the same picture. Introducing paramagnetic material in a magnetic field, you can magnetize it. When the source of the magnetic field is turned off, entropy takes over and rearranges the spins in a random, chaotic way, just as they were before the outside disturbance.