These are delayed registrations of births of Washington. These are filed when a person does not have a birth certificate. The information in these documents contain baptismal records, affidavits to support the claim of the date of birth, census documentation and other misc. information that will support the claim of the date of birth.
The Washington County Name Index doesn't include online versions of the original sources, but can lead you to valuable resources. The research staff at the Washington County Historical Society can help you find more information about this record and other relevant sources.