As you say, 'modern' science was developed in Europe. However, they only hold the distinction because they were 'last.' The Middle East and Asia did do it as well.
There's a variety of theories and factors that people think had an affect. A short list...
1. White people are just better (This one's bullshit, but hey, people think it, so there it is)
2. Europe was, geographically, lucky as hell, because...
a. It's position allowed for trade with just about everyone else, so they got the best of every world at the time, and that eventually led to their dominance in the technological and scientific fields
b. They had some of the best land. The land was very good for agriculture, it had a lot of readily available resources to exploit, and the largest quantity of domesticatable animals/farmable crops. This allowed them to more efficiently survive, which allowed for more people to do engage in pursuits more ambitious then 'keep my kids from starving'
3. Christianity is more conducive to free thought and scientific progress. This is another one I'm not really a fan of, but there is some truth to it. It's true that Christianity is, in modern times, fairly open to technology, but I'm not convinced that's because of any inherent property. It's true that early science was conducted by monks and such, and funded by the Catholic Church, but they also did a lot to hinder it's development and discredit many of Europe's early scientific heroes. And it's not like Judiasm, Islam, and a variety of Eastern religions didn't play a part in scientific pursuits as well. I'm more inclined to believe that, because of outside factors, Christianity is just the religion that happened to be strong armed into giving up and letting science go on without them.
4. Europe's continual, but fairly stable, 'eternal war' state created an incentive to innovate. Basically the 'cultural evolution' argument - Conflict breeds innovation and knowledge, as nothing stokes the fires of the mind like a fight to the death that never seems to end. This has been replicated time and again through history - The most modern examples being the American Civil War, which saw huge leaps in surgical technology and technique, even if we find their methods terrible now; WWII which saw speedy advances in technology across the board, most notably in manufacturing, usable atomic theory and rocket technology; and the Cold War, which saw the Soviets and the US pushing the boundaries of the possible, sometimes in practical terms, and sometimes in pissing contests (We'd probably just be getting around to landing on the Moon if it weren't for Sputnik).
5. Too complicated to ever fully appreciate, and probably a little bit off all the above (Except for the white people one), plus a bunch of stuff I can't think of at the moment.
EDIT: Whoops, meant 'as well,' not 'better.'