If you know how lightning works, a mint is essentially a lightning bank. When a wallet requests a payment via lightning, the mint generates an invoice to receive it and the funds go to the mint, then it gives the wallet ecash tokens representing the amount that was received (kind of like an IOU or a coupon). These tokens can then be sent p2p and at anytime they can be redeemed at the mint, and the mint will initiate a lightning payment for the wallet. I hope this is helpful and not more confusing. The mint handles all lightning transactions for the wallets, and the wallets handle p2p ecash transactions and direct the mint to receive and send lightning payments in exchange for the ecash.