A handset receipt is a delivery receipt generated when the recipient's phone acknowledges the message, the strongest confirmation SMS can give that a text arrived on the device.
When the phone receives the message, it returns an acknowledgement to the SMSC, which forwards a receipt to the sender's gateway. This is the only receipt that proves arrival on the device; it does not prove the message was read, and it is unavailable on routes or operators that stop at acceptance.
Handset receipts also make list hygiene easy: an unknown number fails at the first send with a clear reason, and an absent subscriber is retried until validity expires.
At SMSMeteor: "delivered" means a handset receipt was received; countries without handset receipts are marked on their page, and "sent" is the final positive state there.