For any sensation to take place, the magnet has to exert force on the tissues surrounding it. This happens when the magnetic field of the magnet inside my finger interacts with another magnetic field (or is attracted to a ferrous surface.)
Iron filings can be used to visualize magnetic field lines.
In the case of power transformers (like the one in my alarm clock) the field oscillates with the voltage, at 60 hertz. Unlike a stationary field, which would repel or attract the implant constantly, the changing field repels then attracts, changing 60 times a second. This makes the magnet vibrate. Stronger fields would mean more pronounced vibration. Higher frequencies would cause faster vibrations.
electromagnetic waves like those emitted by antennas. I won't go into the specifics, as I can't really think of a way to explain it without getting very deep into the theory.
If any of this sparked an interest or left you going "HUH?" Wikipedia has great articles on it all, ranging from magnet basics to Quantum electrodynamics.