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Electrons tend to come in pairs when they surround an atom, and especially for smaller atomic weight elements, they tend to try hard to pair up. Now, these electrons are constantly in motion, and a moving electric charge (in this case, say, a spin or circular-esque movement) will produce a small magnetic field.
In most materials, the oppositely paired electron more or less cancels out the field of the other, so, no magnetic field in practice. In some metals however, these electrons can be more stable/common in an unbalanced state. Thus, you get a small magnetic field.
These field directions can often be pretty random. Like, imagine very small pockets going in a random directions all neighboring each other, that due to probability more or less cancel out when you take them as a group. A lot of naturally formed metals can be pretty non-magnetic in this way (yet still interact with magnetic fields). This material can be magnetized however by introducing these tiny random fields to a more powerful field, which can essentially re-align them. And thus, once you have enough of these tiny fields aligned, you get a permanent magnet.
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