The confirmed address simply means the address you're shipping to matches the billing address of a credit card the person has on file with PayPal. This greatly reduces the chance that it could be a fraudulent order.
When you receive the payment you can look at your API response. Depending on which calls you're making it may have the address_status included in the response for you.
If not, you could setup an IPN listener to receive transaction data and that would include the address_status. It would also include a protection_eligibility parameter to let you know whether or not the transaction was covered by PayPal Seller Protection.
The address status is also available in the PayPal transaction details so you could easily see it there any time you're reviewing orders or printing labels through PayPal.
Finally, you could setup Fraud Management Filters in your PayPal profile so that payments without a confirmed address are automatically denied.
If you're using Payments Pro to process cards directly you can look at the AVS response that's included with the API response. It will provide a letter that resembles whether or not the full address matches, just the street address, just the zip code, or no match at all.