As I already stated, no mechanical contact is required for these to work, which means a significantly smaller amount of wear and tear on the braking system. Because of this and their convenience for certain applications, they're used in things like roller-coasters, or industrial applications, and with design modifications they can be used for regenerative braking in electric automobiles.
How does it work? Conducting plates typically have a current create in them due to the movement of magnets, as a result of magnetic induction, which according to Lenz's law, will create a magnetic field opposing the rate of change of flux through the surface. This tends to oppose the motion of the magnet, slowing the device down, and when used properly (such as in regenerative braking), the current induced can be harnessed to recharge batteries. It does also oftentimes produce a lot of heat, which can be negative, but sometimes this can be used to your advantage. If you need to heat something (for example, in pipe soldering), creating an "inductance situation" within something like a copper pipe can heat the pipe until it is ready to be soldered. Or burn stuff.