Here's a slightly simplified explanation:
As the rare earth magnet under the train passes over the fin, an electric current is generated in the copper fin. The electricity that is created in the fin, also has a magnetic field associated with it. The magnetic field that is generated in the fin will always resist the motion of the rare earth magnet on the train. This resistive force is what causes the train to slow down.
A note I will add is that it is the changing magnetic field that creates the electric field in the copper fin.
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