has the option "4 - set the Reset Code". It appears to work, at least both tokens (NEO and 4) accept this command and prompt me for the new Reset code.

The question is - where/when/how can one use it? There doesn't seem to be any application that accepts it???

Please explain how and at what circumstances that code can be used, and what its consequences are: does it just reset the PINs and PIN retry counters? Or does it wipe the entire applet content? Or...?

Reset Code is set with:

gpg --card-edit
admin
passwd
4
[follow prompts from here - you just need to know the Admin PIN at this point, which is 12345678 if you haven't changed it from the default]

For a description of the Reset Code, please see the specifications that the OpenPGP applet is based off of (http://www.g10code.com/docs/openpgp-card-2.0.pdf), in particular page 15. The reset code (or "resetting code" as it's referred to in the documentation) is kind of like the Admin PIN, except the ONLY function it provides is to allow you to reset your PIN if you've locked it out. It can't be used for actually editing the card. It's intended for admins (who know the Admin PIN) to prepare the card for their user, and by providing both the PIN and the Reset Code, it gives the user control over the PIN (and the ability to reset it). If it's for personal / single-user use, the Reset Code isn't really necessary (and that's why there isn't one by default on the YubiKey).

The NEO actually improperly reports that there is a Reset Code counter (look at the PIN retry counter field when you run gpg --card-status or gpg --card-edit - it's the middle number). The YubiKey 4 correctly reports this as - by default, as there is no Reset Code by default.