The Big Wallet is the third proper wallet, able to hold up to 1000 Rupees by itself, double that of the Medium Wallet.
Where to Find
You must give Batreaux 30 Gratitude Crystals.
This is doable after obtaining the Gust Bellows, by completing the following quests: Missing Child, Missing Sister, Cleaning Pipit’s Room. Then collecting at least 10 individual crystals.
(If you wait a little bit longer, two more sidequests will become available.)
You can upgrade the Big Wallet into the Giant Wallet by continuing to give Gratitude Crystals to Batreaux.