The Hanafuda cards are cards forged to locate Oni masks and the ingredients to remove them from faces. They can only be used once per mask.
The cards were located in a holy shrine which was later built over by a car company, but the owners of the company kept the cards and use the symbols on them as the company logo. The Chans soon acquired them and used them to locate the other Oni masks. When all the masks were found, Jade presumed they didn't need the cards anymore and put them in her bag. But when the Oni were released and they ended up imprisoned in Section 13, Jade carelessly threw the cards away, revealing the location of the tenth mask meant for Tarakudo!
It is not known how one can tell how the Hanafuda cards are grouped. Presumably, there are 30 cards, ten sets of three, each card indistinguishable from the other 29. A shortcut to the Hanafuda cards: paint them after you've activated them.