Final answer:
John Winthrop used the term 'covenant' to describe the Puritans' relationship with God, encapsulating their vision of a theologically driven community showcased in the 'City upon a Hill' ideal.
Step-by-step explanation:
The legal term that John Winthrop uses to describe the Puritans' relationship with God is covenant. This concept was central to the theology and community life of the Puritans who settled the Massachusetts Bay Colony. John Winthrop, a prominent Puritan leader, articulated this relationship in his famous speech "A Modell of Christian Charity," delivered aboard the Arbella in 1630. In this address, Winthrop expressed his vision for the new colony as a "City upon a Hill," reflecting a utopian ideal where the Puritan community would live in accordance with the covenant with God, aspiring to be a shining example to the world.