Purchaser goes to Amazon, looks for 'gift cards' and pays ?x, giving recipient's email address as the destination.
Recipient gets an email from Amazon with a string of letters and digits, goes to Amazon, finds 'apply a gift card to your account' in the 'your account' section, and copies and pastes that string of letters and digits. (Or just clicks on the link in the email!) Next time they buy something from Amazon, the first ?x comes from that.
Once bought, the purchaser can't get a refund and all they need to know about the recipient is an email address. Once you've got the string of letters and digits, you can use it with any Amazon account - it doesn't need to have the same email address.
Since a change a few months ago, the recipient gets to see what Amazon thinks the purchaser is called.