Magnetic fields are just relativistic electric fields. And quantum electrodynamics says that the electromagnetic field can be quantized as a photon field. I guess you could say the field is made out of virtual photons (though I wouldn't quite put it that way).
If you are really interested in learning about magnetic fields you need to start at the beginning. It just does not make sense to start with the explanations provided by relativity, when the beginner has no idea of either electromagnetism or relativity.
Unfortunately there is no 2 sentence, or even 2 page explanation which can do the subject justice. I would recommend that you find a used copy of something like Halliday & Resnick. Start at the beginning of the Electromagnetism section and read carefully. If you do not have a math background which includes calculus then you may find the reading difficult.