If you pay a merchant, and the merchant claims to not have received the funds, you may need to prove to a third party you did send the funds - or even to the merchant, if it is a honest mistake. Monero is private, so you can't just point to your transaction in the blockchain, as you can't tell who sent it, and who received it. However, by supplying the per-transaction privatekey to a party, that party can tell whether that transaction sent monero to that particular address. Note that storing these per-transaction keys is disabled by default, and you will have to enable it before sending, if you think you may need it:
Pass in the transaction ID you want the key for. Remember that a payment might have been split in more than one transaction, so you may need several keys. You can then send that key, or these keys, to whoever you want to provide proof of your transaction, along with the transaction id and the address you sent to. Note that this third party, if knowing your own address, will be able to see how much change was returned to you as well.
Replace `TXID`, `TXKEY` and `ADDRESS` with the transaction ID, per-transaction key, and destination address which were supplied to you, respectively. `monero-wallet-cli` will check that transaction and let you know how much monero this transaction paid to the given address.
