Napoleon Bonaparte was a skilled military strategist, and his keen intelligence lead him to great success in the unification of France after the Revolution. His rise to power began with his leading armies to victory against the Austrians in Italy, and then in the invasion of Egypt. In 1799 he was made first consul of the new consulate, which made him the head political figure of France. He instituted a number of reforms in social, legal, and administrative matters and centralized the French government. He brought much relief to the French republic, who had suffered in the disorganization which followed the downfall of the monarchy. Unfortunately, Napoleon's success made him blind to the possibility of defeat. The French army was spread thin while engaged in war in the Iberian peninsula and simultaneously attempting to invade Russia. Napoleon sought to expand the French empire, but he was defeated in 1813 at the Battle of Liepzig by forces from Prussia, Russia, Austria, and Sweden. He retreated to Paris and was there forced to abdicate the throne for his failure. He was exiled to the island of Elba and escaped a year later to return to France for a sort of "victory lap." He intended to give another go at leading France to imperial victory, but was defeated at the Battle of Waterloo. As punishment for this failure, he was again exiled to an island, where he died.
One of Napoleon's lasting impacts on the world was the decision to sell the Louisiana territory to the United States in effort to raise funds for the war he planned to wage throughout Europe. If he had not sold this territory to the then-small United States, it might still be French territory today. The acquisition of the Louisiana territory encouraged a new wave of expansion and exploration into the American west.
Much of Napoleon's reforms persist today, particularly the effects of the Napoleonic code, which made all French citizens equal at birth and demanded freedom of religion. The Napoleonic code served as a template for the legal systems of many nations formed after the Napoleonic Wars.
Napoleon's reign also had the effect of spreading the values of the French Revolution (freedom, equality, and brotherhood or nationalism) to areas beyond France and even outside Europe. These ideas helped spur revolutions across Europe, and combined with the Napoleonic code are at the basis of a number of legal systems around the world.
Because it is such a popular myth, I'd like to address whether or not Napoleon's armies actually shot off the nose of the Great Sphinx. While it's a great story, sketches made 50 years prior to Napoleon's invasion show the statue already without a nose. A 15th century source credits the disfigurement to Muhammad Sa'im al-Dahr, who saw the practice of praying to the Sphinx for a good harvest as idolatry. In 1378, he was so angered by this act of devotion to a false idol, that he knocked off the nose and was hanged for his crime.