This is an enormously complex question, but if we narrow it down first to the political changes that took place, other factors—social and economic, for example—can be partly dealt with as well.
The defeat of France in the Seven Years' War (in its American theatre known as the French and Indian War) resulted in Canada being taken over by the British. In 1763, France thus ceased to be a power on the North American mainland, with Louisiana also taken from it and turned over to Spain. The British expected their colonists to pay part of the cost of the war, the rationale being that the war had been fought to protect the English settlers. This led to a series of taxation schemes that caused huge resentment in the colonies and led to the War of Independence from 1775 to 1783. With independence the following major political and social changes took place:
1) The states north of the Mason Dixon line enacted laws, either immediate or, in most cases, gradual, abolishing slavery and liberating the enslaved people within their borders.
2) State constitutions were written which provided for religious freedom in those states where it was not already explicitly granted. Other vestiges of British rule, for instance, inheritance laws such as primogeniture, the right of succession to a first-born male child, were abolished.
3) In 1787 the Constitutional Convention met in Philadelphia and planned the new government, superseding the Articles of Confederation and establishing the system we still have. It was basically unprecedented in its division of power among executive, legislative, and judicial branches. Instead of copying the English Parliamentary Constitutional system, the US founders created a new system designed to limit the power of any single entity of government.
4) In 1789 the new government was initiated with Washington as President. In the following decade, the disorders and wars in Europe started by the French Revolution had a kind of ideological spillover into the new US, creating extreme factionalism between the Federalists, who considered the War of Independence to have been a family quarrel with the British and now favored an alliance with them, and the Democratic Republicans, who favored an alliance with Revolutionary France. By the end of the century there was no real resolution to this issue and the heated partisanship it had evoked.
5) White settlement west of the Alleghenies accelerated with the independence of the US. During the war from 1775 to 1783 the Native Americans had mostly sided with the British, who had (presumably) wanted to reserve the lands west of the Appalachians for them. The British did not evacuate their forts in the Northwest Territory for several decades after independence, and the Native Americans became more dependent on the protection of the British against the settlers. But in the battles between US forces and Native Americans in the 1790s, the British did little to help the indigenous people.
The above are key points, but are basically a sketch of the changes that took place. You might wish to look into the very beginnings of industrialization in the US, and the way entrepreneurship in general was encouraged by independence. In addition, the white colonists were hardly a monolithic entity themselves. You might research what course was taken by those who had been Loyalists during the War of Independence and wished to remain under British rule. One might also ask what conflicts existed among the different ethnic groups—English, German, Dutch, French Huguenot, Scandinavian—and also the conflicts between rural and urban people and the local wars such as the Whisky Rebellion. And finally, how and why did slavery continue to expand, despite the provision in the constitution that the slave trade would be ended in 20 years (by 1808)? How significant were all these factors in the growth and changes of the new country?