we don't know why or how there is electric charge (and their related fields), we just know that there is electric charge; it's one of the properties of the universe; same with gravity. We have uncovered mathematical laws of charge and and their relationship (via div, grad, curl and all that) to magnetic fields, but we don't know how or why, just what is.

My source is Feynman.

I believe GP is a riff on the common joke among physicists: "Anyone who claims to understand quantum mechanics is either lying or crazy."

To be more specific in the case of magenetism, you can say that, for example, ferromagnetism arises from the alignment of magnetic moments into cohesive domains, where the individual magenetic moments arise on the atomic level from unpaired electrons in the d or f orbitals.

But if you poke at that (incomplete) answer a little bit, things start to get complicated. How exactly do magnetic domains align? What if there's a disruption in crystal structure? Are there other sources of magnetic moments? Where does the magnetic moment on an elementary particle come from? The answers to these questions get pretty complicated and questions like these motivate a lot of active scientific research.