Even if you studied it, the answer boils down to “magic”.
You take these magnets, and move them around these long snakes of metal (because electrons can move easily through metal) and that makes the electrons in the wires move.
Okay, why does moving around a magnet near metal make something inside it move?
Well there’s something we call the “Lorentz force” which basically pushes a magnetic thing in a specific way if you move another magnetic thing around it