Try to pick up a penny with a magnet. Can't do it, can you? And yet as the person in the video moves a magnet close to a copper penny, the penny slides in the direction of the magnet's motion. What we have here is a perfect illustration of the interrelationship between electricity and magnetism. While copper is not a ferromagnetic material -- that is, it cannot be readily magnetized, and it will not be attracted to a static magnet -- it is a really good conductor of electric current.
All magnetic fields are actually the result of moving electric charge. In the case of a permanent magnet, the moving charges are electrons in motion around their respective nuclei. The moving electrons produce magnetic fields. While these atomic-scale fields are generally exerted in random directions, and tend to cancel each other out on a macroscopic scale, it is possible to align these fields, by placing the material inside an external field.
Electric currents in wires also produce magnetic fields due to the moving electric charge. To prove this to yourself, try this at home: take a battery, a compass, and some copper wires, with the wires disconnected from the battery. Place the compass underneath one of the wires, orienting the wire so that the needle is parallel to it. Now connect the wires to the battery terminals. The compass needle deflects, because as soon as the charge in the wires starts to move, a magnetic field is generated.
So what is happening when the magnet is moved past the penny? The penny obviously feels a force. This is because even though the coin has no permanent static magnetic field, the moving magnet induces an electric current in the penny, by the principle of electromagnetic induction. (A changing external magnetic field within a closed loop of conducting material will cause an electric current to flow in the loop.) Electric current in the penny means the penny will now have its own magnetic field, and will therefore experience a force from the magnet's field.
Adam Weiner is the author of Don't Try This at Home! The Physics of Hollywood Movies.