This is common for serving subsequent documents after a case has started (like motions or answers) or for specific types of cases where personal service is not required.
To be valid, the affidavit must typically state exactly what documents were enclosed, the address they were sent to, and that postage was fully prepaid. In many jurisdictions, this affidavit is accompanied by a Certified Mail receipt or a Return Receipt to provide a physical paper trail that the envelope was actually delivered or at least attempted. It prevents the recipient from claiming they never received the paperwork necessary to defend their case.