PayPal Payment Review is a free fraud-detection feature that notifies merchants using PayPal PayPal Express Checkout of potentially high-risk payments, offering increased protection against processing and shipping fraudulent orders.
When a transaction is flagged by PayPal as high-risk, it will be marked as being under review beside a new "Payment Review" field in your Order Manager. PayPal will also alert you to the status of this transaction via email. The transaction will then be investigated, and PayPal will either process the payment, or deny the transaction and reverse the funds. You will usually be notified of the payment review resolution within 24 hours, both by email, and with either an "OK to ship" or "DO NOT ship" status message in your Order Manager.

Payment under review

Payment processed – the order may be shipped

Payment denied – do not ship this order
If the Payment Review Status does not automatically update, you may check the status using the "Check Payment Review Status" button, located at the bottom of the Order Details screen.

"Check Payment Review Status" button in Order Manager
Transactions that clear Payment Review may be eligible for PayPal's Seller Protection Policy, which covers you against chargebacks for items that aren't received, and for unauthorized payments and payment reversals. To qualify for Seller Protection, you must meet PayPal's Seller Protection Policy conditions. Learn more.
Questions regarding PayPal Payment Review and the payment review status of an order that has been flagged for review should be directed to PayPal. For more information about PayPal Payment Review, please visit PayPal's Frequently Asked Questions page.
See also:
What is the Payment Review Status for orders placed using PayPal?
What is PayPal Seller Protection?