What does O'Sllivan when he says it is "our manifest destiny to overspread the continent allotted by Providence?"

I think John O'Sullivan means that population is too big and they need to constantly get bigger and expand - God's wish.

John Louis O’Sullivan, a popular editor and columnist, articulated the long-standing American belief in the God-given mission of the United States to lead the world in the transition to democracy. He called this America’s "manifest destiny." This idea motivated wars of American expansion. He explained this idea in the following essay where he advocated adding Texas to the United States.