It is important to remember that the French and Indian War, which lasted from 1754-1761, was part of a much larger global conflict, known as the Seven Years' War, a massive struggle between Britain and France for control of colonies around the world and for increased influence in Europe that lasted from 1756-1763. Essentially, the major, direct result of the French and Indian War in North America was that France ceded, in the Treaty of Paris in 1763, all of North America east of the Mississippi to Great Britain. This included Canada, almost all of the West Indies, and all of the disputed area in the northwest. The British even got Florida, a Spanish possession, because Spain had allied with the French in the conflict. So the short-term impact was that British America doubled in size.
In the long term, the results of the conflict were more complex. Generally speaking, it led to increased tensions with Britain's American colonies. Hoping to avoid having to send troops to settle costly border conflicts, the British declared, in the Proclamation of 1763, that all lands west of the Appalachians were closed to American settlement. This was a major disappointment, not so much to common people (who tended to ignore the proclamation) but to land speculators who had secured promises of massive grants of land in the region that they could no longer sell. Probably the largest of these speculators was George Washington. The war also created a spirit of unity among the colonies, expressed by the proposed Albany Plan of Union in 1754. Finally, and most famously, Parliament attempted to pay for the massive debt accrued in financing the war by levying a series of taxes on the colonies. The first of these, the Sugar Act, met with great opposition which only intensified with the passage of the Stamp Act in 1765.