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 private key 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:
