All a PayPal transaction ID does is identify the PayPal transaction. You can put the ID in the search box on the PayPal website to find the payment and see the details like date, amount, etc.
If your PayPal account is set up where you have to manually claim each payment, once notified of payment you'll need to head to PayPal to accept the payment: Log into PayPal. Go to Summary. Under 'Pending', next to the message showing the recipient 'hasn't accepted yet', click Approve.