When ICP became a meme for not knowing how magnets worked, I didn't participate. Nobody really knows how magnets work. Everyone just assumes scientists know how magnets work and that it's known, even when everyone making fun of ICP (not that there aren't things to make fun of them for) didn't know themselves how magnets work.
But the kicker is, nobody knows how magnets work. Keep asking how and keep getting deeper into it and you hit a wall of "it's a fundamental force". So the best answer to the question of how a magnet works is the same as how a posi-trac rear end on a Plymouth works. It just does.