In 1820, Oersted discovered that current flowing in a wire produces a magnetic field around the wire. In 1831, Faraday discovered that if you move a wire through a magnetic field, it "induces" electricity to flow in that wire. In basic AC induction motors there are no permanent magnets, the magnets are electromagnets. If you applied DC, the magnetic fields would be expand around the wires (coils) when you first energize them, then stay that way, so nothing would move. With AC power, the current going into the electromagnets is constantly changing from zero, to full positive, to zero, then full negative, then repeat. All the while, the magnetic fields in those coils are then expanding, then collapsing, then expanding again, over and over. So by virtue of that relative "motion" of the magnetic fields moving across the rotor bars as they expand and contract across them, they induce current to flow in them. The current flowing in the rotor bars then creates its own magnetic fields, which are in opposition to those in the stator, repelling from one another and making the rotor spin.