It means that religion provided a feeling of security and certainty that the social structure was correct, just and ordained by God for the good of mankind. The Church and the gentry were held to have been granted their positions by God for the guidance and protection of those beneath them who were incapable of making sensible, informed decisions for themselves. Loss of faith in religion and exposure to other beliefs and ways of life have eroded that certainty in the "divine" structuring of society.

A single, public religion (versus plural, private or individualistic values) had been the unifying force. Secularization (the introduction of plural, private and individualistic values) challenged the role of religion in society and is the hallmark of modernity.

Not altogether different from what Jack has said, though rather than being an "embracing" influence I think of it as an "infusing" and thereby "undergirding" or "all-pervasive" influence.