What does it mean to get married through official documents?

This sentence means marriage registration certificate.

In ancient times, official documents refer to official correspondence, which is a kind of official documents in ancient China. It is the general name of the documents used in writing between feudal officials in past dynasties. After the wedding ceremony, you need to go to the relevant government agencies, such as the Civil Affairs Bureau and the registration office, go through the marriage registration formalities and get a formal marriage certificate or marriage registration certificate.