Taking online payment is great; it means we can process orders quickly. However, not all customers want to pay online. For smaller, less-known e-commerce sites, customers may not trust supplying their card details. We may wish to enable customers without credit cards to make purchases from our store. This is where offline payment comes in.
When the customer confirms their payment method, and confirms the order, we simply mark the order as "pending payment", and inform the customer of how they can send payment, be this by check, in person, or perhaps through card over the phone, along with a reference number. Then when we receive the payment, we simply mark the appropriate order as "paid".