How do magnets work?

Magnetism originates with electrons, which behave as tiny magnets due to a quantum property called spin plus their orbital motion. In most materials, those individual electron magnetic moments point in random directions and cancel each other out, leaving no net magnetism. In a small set of materials, iron, nickel, cobalt, and certain alloys, quantum interactions between neighboring atoms cause electron spins to align with each other across regions called magnetic domains. When the domains themselves are randomly oriented, the material is unmagnetized; align the domains, by exposure to a strong field, or by manufacturing, and the material becomes a permanent magnet with north and south poles.

Moving charges and magnetism are two faces of one thing, electromagnetism, unified in the nineteenth century by Maxwell's equations. That connection is why running current through a coil of wire creates an electromagnet you can switch on and off, and why moving a magnet near a coil generates current, the principle behind essentially all electricity generation, motors, transformers, and hard drives. Earth's magnetic field, generated by circulating molten iron in the outer core, is what orients a compass needle and deflects much of the solar wind, a genuine prerequisite for the atmosphere we have. Heating a magnet past a threshold called the Curie temperature randomizes the domains and destroys the magnetism, and striking one hard can partially do the same, which is why dropped magnets weaken.