It wasn't their intelligence, because many outside nations had no problem in adapting to western technology.
Also the reasons for Europe rising above the rest of the world are a complex set of factors that cannot be explained with a racist belief, not backed by evidence. There are two things that made Europe marginally more successful:
The first is due to the fact that the rough waters of the North Sea forced Europeans to adapt to better ship building. Fellow Europeans over in Rome however had worse ships because the Mediterranean has much calmer waters.
The second is a complex set of steps that led Europe to a different path from the rest of the world. There are two important things to know. First is the European identity, and second how it affected the development of the continent later on. The West is identified by three pillars:
Next is the destruction of feudalism, rise of Absolutism, and the struggle between the crown and the Church. Why?
The Black Death.
Of course, China had a black death as well. However, they suffered 200 years of Mongol rule, causing a conservative shift in the nation for the next dynasty, closing off from the rest o the world and shunning merchants.
Europe, however, was cleansed from overpopulation experienced during the High Middle Ages allowing for feudalism to get out of fashion. This made farmers and serfs move into cities, under the direct taxation of the king strengthening the crown in the fight against the Church. With stronger towns merchants flourished and especially in Italy made so much money that these rulers would fund expensive art projects starting the Renaissance. The Church did originally fund the sciences, however the Protestants didn't so they "reformed" by suddenly hating science. This would be just another middle finger to the Church as thanks to the crown science continued, this time with the freedom to not require the Church for scientific inquiry. The nobility also suffered from the lack of serfs allowing for more serfs to move into the cities in an endless cycle.
With a new love for science and capitalism and extremely effective ships it was a given Europe would go on to conquer the world.