Read-only feature:

Unlock a special piece of battle music / Receive higher-quality items and materials

Scan at the monastery's amiibo gazebo to spawn a variety of random items and materials once per in-game month (combined with the generic functionality).

Scan (regardless of the in-game-month limit) to receive character-specific pieces of music, which you can then choose in the options menu during battle.

Sources: Nintendo of Japan, GameXplain (video), Arekkz Gaming (video)


Read-only feature:

Receive items and materials

Scan at the monastery's amiibo gazebo to spawn a variety of random items and materials once per in-game month (combined with the character-specific functionality).

This feature works with any amiibo (with the possible exception of those that work with its other features).

Sources: Nintendo of Japan, GameXplain (video), Arekkz Gaming (video)