I remember a demonstration of this concept in an undergraduate electrical engineering class. The class demonstration featured two aluminum pendulums. One of them had a solid flat sheet of aluminum at the bottom, and the second was in the same shape but with slots going through it, making them look more or less like solid and slotted spatulas that have been flattened. When a strong magnetic field is applied (permanent magnets in this case), a strong braking force on the solid pendulum results, while minimal braking force results on the slotted pendulum. The idea is that the movement of the conducting metal through the magnetic field induces an internal electric current (the "eddy" current), which essentially converts the kinetic energy of the pendulum to heat. The continuous sheet of aluminum experiences much stronger braking force because the internal electric currents are unrestricted, while the slots in the other sheet of metal limit the eddy current and therefore reduce the braking force.

To use this concept on a bicycle, magnetic rim brakes may not be feasible because I don't know if the magnets would be close enough together to get a strong enough magnetic field, and I don't know if spoke holes are likely to cause problems by breaking up the eddy currents. Magnetic disk brakes seem more plausible, but there may still be challenges posed by putting strong magnets right next to the spokes, and you definitely need a solid aluminum disk, so existing brake discs wouldn't work.