Althought truthfully I don't think I have ever heard an explanation for magnets that didn't go
There's a force called magnetic (that exists perpendicular to the electric)
or something about partially filled valence electron shells being able to acquire unequal amounts of spin or something like that.
Honestly, If Magnet's weren't so demonstratible, most people would call those explanations lacking (as it is , the explanations are still lacking and for the most part people are content with 'there you can see that it infact does work' ).