When you create any type of transaction within NPE, you will create an invoice. This is used as both a form of receipt for financial purposes and as a way to send invoices for payment if needed.
Invoices also give you the ability to enter multiple donations in one transaction for a contact, for those situations where they pay for both with the same payment method. You can also use invoices to record multiple transaction types - ie, a Membership and a Donation - and record that they were paid for together.
If you have a donation you don't yet have payment for, it should be entered as a Pledge instead.
In short, if you don't send invoices for donations (or any other transaction), then you can disregard invoices. Invoices allow you to record multiple transactions in one payment, send receipts and invoice unpaid transactions.