If you have a strong enough magnetic field all matter is magnetic. But copper is so weakly magnetic that we can't observe it without very, very large magnetic fields. So the short answer is "No, copper isnít magnetic." This can quickly be tested by trying to pick up a penny with a magnet.
But copper will interact with magnets in fascinating ways.
The interaction of copper with a magnet in the video is based on Lenzís Law. The details require some physics knowledge but the basic idea is pretty simple.
Aluminum is works almost as well as copper (and is much cheaper).
Magnetism and electricity are closely related. When a magnet moves near copper (or other metals) it sets up electrical eddy currents.
The eddy currents will repel the magnet as it falls down the copper tube. This repulsion pushes against the magnet and slows it down. In the video you can see that the magnet appears to float through the tube.
So, Is Copper Magnetic?
The answer is that copper itself is not magnetic or is only slightly magnetic (not big enough to see under normal situations). But it does interact with magnets and that's pretty important. It is this interaction with magnets that power plants use to generate the electricity we use every day. It also makes for a very, very impressive demonstration.