A second thing I don’t understand about magnetism

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.