Since paypal plugin 1.3.0 logged-in users can choose to pay by check. When they validate their order, the system create a private IPN and the status of there purchase is pending. They can't download the product if the product is downloadable, and they are not added to a group is the product is a subscription.
When admin receive the payment by check, he need to valide the order. For this go to the transaction page. Link is in ID column on the Purchases page.