For instance fundamental charges are a lot like positive and negatively-oriented vortices in a fluid, which when they touch cancel each other out and radiate energy away. They're not _exactly_ like that, but they're a lot like it, and that's a model people can understand without knowing the first thing about quantum field theory. Sure, you won't understand from that why like-charges repel each other, not really, but if you play with the analogy for a while it starts to seem why that might be true as well.
(See https://www.ribbonfarm.com/2015/09/24/samuel-becketts-guide-... for some pictures of this... I wish I had better though.)
Magnetism is quite a bit trickier to explain in this model but it can done with some work. In particular: a charge radiates little linear packets of energy just by existing; when one of these packets hits another charged particle it moves a tick closer or further away (based on +/-). A current/moving charge/magnetic dipole radiates away little spiraling packets of energy which are aligned in the plane orthogonal to the conventional magnetic field; when these hit another charged particle they get rotated a tick.