It is interesting how many sites quote these particular lines, but provide no context, or even bother to cite the origin. Most of them do so with the obvious intent of saying that the US is a religious country, and has to be a religious country because John Adams said it had to be religious country. It's useful to look at it in context.

It's from his address to the Massachusetts Militia in October of 1798:

While our Country remains untainted with the Principles and manners, which are now producing desolation in so many Parts of the World: while the [ USA ] continues Sincere and incapable of insidious and impious Policy: We shall have the Strongest Reason to rejoice in the local destination assigned Us by Providence. But should the People of America, once become capable of that deep .... simulation towards one another and towards foreign nations, which assumes the Language of Justice and moderation while it is practicing Iniquity and Extravagance; and displays in the most captivating manner the charming Pictures of Candour frankness & sincerity while it is rioting in rapine and Insolence: this Country will be the most miserable Habitation in the World. Because We have no Government armed with Power capable of contending with human Passions unbridled by morality and Religion. Avarice, Ambition ,Revenge or Galantry, would break the strongest Cords of our Constitution as a Whale goes through a Net. Our Constitution was made only for a moral and religious People. It is wholly inadequate to the government of any other

It is comparatively easy these days to split off "moral" from "religious". But in this period ( and well into the 20th c.) to say someone was spiritually-guided carried an assumption they were morally-guided as well. Religion was thought to be the main impetus to virtue. Some philosophers like David Hume could argue against that, and show by example that the two did not have to be linked, but the notion of a moral atheist was pretty rare: most people would believe that the only thing that kept humans from doing terrible things was their fear and love of God. Here Adams is using the terms together to make an argument for the Constitution very common to the 1790's: that its success depended upon the active participation in the government by law-abiding honest people. But it also shows one concern that Adams had in particular. Many of the founders, like Madison and Jefferson, thought of Americans as being relatively equal, and content to be equal. Unlike them, Adams ( after the Revolution) thought that humans tended to strive for superiority, and that, even without a hereditary aristocracy in the US, there would arise an aristocratic elite and an unruly mob wishing to loot and supplant it. He was pretty comfortable with the idea of that elite class being a good force ( maybe here, more "armed with Power" ) perhaps even thought the US could have the equivalent of a House of Lords. He thought that the balancing of powers in the Constitution also provided some defense against the conflict, but he was always very uneasy about the danger of mob rule. In 1798, he would be quite aware of the French Revolution "producing desolation": that certainly would have put him in mind of the possibilities of a populace no longer moral and religious.

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John Adams : A Defense of the Constitutions of Government of the United States: https://books.google.com/books/about/A_Defence_of_the_Constitutions_of_Govern.html?id=aH0NAAAAYAAJ&printsec=frontcover&source=kp_read_button#v=onepage&q&f=false