Here is a picture from Wikipedia about how eddy current braking works
(1) Conductor rotating in an external B field, in green, induces circulating currents in the conductor - the generator effect. (2) These circulating currents generate a magnetic field, in Blue, in accordance with Lenz's law to oppose the direction of the change in flux.
Now, I don't understand how an induced $B$ field, blue arrows, slows down the rotating disk. I can see that the direction of induced $B$ field on left side points up and the right side points down. This induced field interacts with the external field, in green, but I can't see how this interaction results in a braking force in the direction opposite to the motion of the disk.