Freedom is, on this model, freedom to do good. And good is defined as actions in accordance with God’s will. Unfreedom comes from sin, or from subjection to Satan’s power. Our natures, though fallen, are still essentially oriented towards this variety of good. We are free to pursue our true natures only when we escape the influences of sin.
Depending on the specific interpretation of some of the finer points of puritan theology, this form of freedom may amount to something very like a complete surrender. The varieties of puritanism which most emphasize the competely “free” nature of God’s grace–it’s entire disconnection from any acts on our part–push this version of freedom to a point worlds away from most modern varieties, which emphasize individual autonomy and freedom of choice.
For a careful statement of the doctrince, see John Winthrop’s speech On Liberty.
[see Foner’s Story of American Freedom, ch. 1)