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.
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.
Now we have better ideas about how electricity works, we tend to talk about current as a flow of electrons, from negative to positive, in the opposite direction to the conventional current. When you are trying to figure out the rotation of a motor or a generator, be sure to remember that current means conventional current and not electron flow.