Copper is a diamagnetic material. Diamagnetism is a property that all materials have, but it is so weak that we call diamagnetic materials as non-magnetic.
What you see here is a strong magnet creating a changing magnetic field near Copper.
Since Copper is an excellent conductor, the changing magnetic field induces currents in it. These currents, in turn, create a magnetic field opposing any changes in the magnet’s magnetic field. Hence, we get magnetic repulsion.
Inducing the currents (eddy currents) also consumes energy. That’s why there seems to be a braking effect when you try to slide a magnet down a Copper plate. It’s not friction. It’s potential energy being turned into both kinetic energy and electromagnetic energy (eddy currents).