What does George Bancroft think is the role of the people in Government, and who does he mean by the people?

Bancroft believed, rather fervently in fact, in popular sovereignty. The role of the people in government was to participate in it, and to shape it according to their will. He placed great emphasis on the fact that American government was based upon the will of the people, singing its praises in his History of the Colonization of the United States:

At a period when the force of moral opinion is rapidly increasing, they [the United States] have the precedence in the practice and the defence of the equal rights of man. The sovereignty of the people is here a conceded axiom, and the laws, established upon that basis, are cherished with faithful patriotism.

Bancroft viewed the representative nature of American government as one of the things that made it exceptional compared to the rest of the nations in the world, and he saw the nation as an example to liberal nationalists in Europe. But Bancroft was also very much a man of his time (most of his major writings were published before the Civil War). For Bancroft, "the people" were white males, though he did not approve of older political distinctions based on property ownership. For him, "democracy" was something like that promoted by Andrew Jackson, which enfranchised most white men—but nobody else.
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