A second thing I don’t understand about magnetism

Standard
Magnet

Image via Wikipedia

Magnets attract (or repel) one another. But how?

How does the electromagnetic force get turned into kinetic energy? Do all the electrons inside a magnet ‘rush’ to one end of the magnet – if so why don’t we see an imbalance of charge (or maybe we do – after all magnets can be used to generate current).

Fear these questions may lead some of you to doubt I have any sort of physics qualification at all – but I do not recall being taught any of this, at ‘O’ level, ‘A’ level or as an undergraduate.