If you are looking mostly at the Puritans, the importance of religion was that the church played a central role in people's lives. The Puritan church was established in the colonies of New England and church leaders held temporal power as well as religious power.
The Puritans gave the leaders of the church power over almost every aspect of community life. As the link below shows us, the church elders had the power to do things like banning dancing and playing cards. They even had the power to take children away from families who were not raising them in ways the church accepted.
The fact that the New England colonies were willing to give this kind of power to the church shows the importance of religion in 17th century America.