Vouchers are useful when Alice wants Bob to pay her in a secure tamper proof way.
First she asks Bob what is his account address, she then logs into the wallet using Bob's address and using the normal send money dialog performs a payment from Bob to her account.
But of course she cannot submit this payment since she doesn't have Bob passphrase.
Instead she enters her passphrase and checks the voucher checkbox. As a result the wallet generates a digitally signed voucher she can send to Bob as a json file or QR code. Nothing is submitted to the blockchain at this stage.
Bob now uses the "Load Voucher" function from the wallet gear menu to load Alice's voucher. He double checks all the details then signs and submits voucher to the blockchain.
The result is that Alice received her payment while Bob now has the voucher which represents an invoice for his financial records. Alice got her tokens and Bob is sure that he really paid Alice and that Alice indeed has a passphrase to her account.