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The large scale magnetism, like the kind observed in bar magnets, results from magnetic fields that naturally radiate from the electrically charged particles that make up atoms. The most common magnetic fields come from negatively charged particles called electrons.

Every electron generates a magnetic field, but they only generate a net magnetic field when they all line up. Otherwise, the electrons in the human body would cause everyone to stick to the refrigerator whenever they walked by.

According to the classical theory, magnetic fields are clouds of energy around magnetic particles that pull in or push away other magnetic objects. But in the quantum mechanics view, electrons emit undetectable, virtual, particles that tell other objects to move away or come closer.

We just observe that when you make a charged particle move, it creates a magnetic field and two poles. We don't really know why. It's just a feature of the universe, and the mathematical explanations are just attempts of getting through the ‘homework assignment’ of nature and getting the answers.