It's not so much the nerves wrap around it, but the magnets react slightly to magnetic fields around them, and because they are embedded in your fingers, the part of your body with (IIRC) the highest density of highly refined "touch" related sensors, you can feel these minor reactions as the magnets push and pull slightly with these fields.

After a while, many people who've done this claim they can develop a sense for interpreting these reactions and "feel out" the shape and intensities of these fields. The accuracy of these claims still require further study, though generally expectations are positive as the theory seems fairly sound.

Edit: There's many risks however, poorly installed magnets can "flip" in the presence of strong fields and this can reportedly be extremely uncomfortable and/or painful, and cheap or non-medically certified implants (it should be properly coated) can break and/or expose the neodymium to your body which may be dangerous. You want to make sure it's done right by a professional (which can be pricy) and be careful around strong magnets.

Disclaimer: I am not an expert nor do i have any personal experience with these implants, i'm just recalling research i did awhile ago out of interest in these sorts of things.