A simple, experimental motor such as this is not capable of making much power. We can increase the turning force (or torque) that the motor can create in three ways: either we can have a more powerful permanent magnet, or we can increase the electric current flowing through the wire, or we can make the coil so it has many "turns" (loops) of very thin wire instead of one "turn" of thick wire. In practice, a motor also has the permanent magnet curved in a circular shape so it almost touches the coil of wire that rotates inside it. The closer together the magnet and the coil, the greater the force the motor can produce.
Think of the atoms of magnetic material as an unruly herd of cattle. Running electric current through the material will polarize these atoms, creating the magnetic field. But as I mentioned, this is an unruly herd, so it takes time for the current to bring all those atoms into formation.
If you place the wire near a permanent magnet, this temporary magnetic field interacts with the permanent magnet field. You will know that two magnets placed near one another either attract or repel. In the same way, the temporary magnetism around the wire attracts or repels the permanent magnetism from the magnet, and that is what causes the wire to jump.
Another interesting design is the brushless DC (BLDC) motor. The stator and rotor effectively swap over, with multiple iron coils static at the center and the permanent magnet rotating around them, and the commutator and brushes are replaced by an electronic circuit. You can read more in our main article on hub motors. Stepper motors, which turn around through precisely controlled angles, are a variation of brushless DC motors.