Winthrop means that they (Puritans) must remember that they are different from the rest of the world.
Explanation:
By the lines in bold, Winthrop means that they (Puritans) must remember that they are different from the rest of the world. The phrase "as a city upon a hill" portrays the idea of a distinct and looked upon city in the world.
These lines reveal the Puritans belief in religious intolerance. They propagate that religious differences should not be tolerated. Therefore, they want to build a city/community where there is no other religion but only Puritans.
