As more settlers came to America, the need for cheap/free land was overwhelming. Going north was possible, but most thought the better land was to the west. And those pesky French had settlements to the north. Going south (Florida) was possible, but the overwhelming bulk of thought at the time was hot swampy areas were unhealthy. So basically, expansion had only 1 direction to go. Westward.
People forget that the bulk of European immigrants arriving in America were dirt poor. So poor in fact that they were indentured servants for 7 years, just to pay for passage to America. Of course, there chances of ever being a landowner in Europe was close to nonexistent. And the hordes of immigrants seeking a better life continued.
Of course, this put the new settlers on a collision course with Native Tribes who occupied the land. During Colonial times. Natives were unquestionably the best fighters on the planet. They used stealth to blend in with the forest and unlike Europeans, who fought in formations, used guerilla war tactics. However, Europeans had massively more modern technology. The wheel, metal tools & firearms, along with the Europeans abilities to shift Tribal alliances to there benefit, meant doom for the Natives. In time, the Manifest Destiny took hold with religious fervor.