There are a few factors to take into consideration in order to understand why Western Europe was able to rise as the dominant region of the world. First, we should consider that Europeans had developed greater immunity to certain diseases that were common in Europe. An example of this would be smallpox. When Europeans arrived in the Americas, they brought smallpox with them, but the natives did not have the immunity that the Europeans did, and this killed off many natives.

Another factor to consider is technology, particularly the use of gunpowder. While gunpowder was invented in China and had been in use in Asia, it was Europeans who really harnessed its true power. Gunpowder led to the use of guns and cannons, which could be utilized in multiple ways in war, including in forts and on ships. One theory argues that these improvements came about as a result of greater control by European kings and their ability to tax. With European governments able to collect more money through taxes, they were also able to spend more on military weapons. They learned from their mistakes and made improvements, which led to a strengthening of the military power of Western European kingdoms.

Another factor many consider as contributing to Western Europe's domination of the globe would be the fact that Western Europe was the first to industrialize. This, however, was more of an occurrence after colonization had already begun. It may serve to explain how Western Europe was able to remain dominant for so long, though.

Finally, I think it is important to consider the motivation behind all of this. As the Middle Ages came to an end, and kings began to establish more powerful nation-states in Western Europe, wealth became an indicator of strength. As Europeans discovered the vast resources available around the world, kings realized controlling these resources could further wealth. It is due to this that many European kings were motivated to spend money and engage in conflict to gain new overseas territories.

The answer to your question lies in the unique political geography and history of Western Europe. No other continent has so many separate nations who are independent and at times antithetical to each other, yet geographically close to one another. The end result of this situation has been that more wars between nations have been fought in Western Europe than any other continent. As weapons are necessary to fight wars, and superior weapons are needed to win wars, the nations of Western Europe devoted much more time, effort and expense to developing superior weaponry than did those of any other continent.  When Europe began its expansion into other areas, it used this superior weaponry to its manifest advantage. Among the advantages, of course was firearms against which hand weapons were practically useless. European diseases also proved devastating to those who encountered Europeans for the first time. Other areas of the world did not have the weapons to compete with Western European weaponry, and were sadly susceptible to European diseases and to which the Europeans were immune. These several factors led to the domination of Western Europe during the Age of Exploration.  

For further information, you might consult Jared Diamond's Guns, Germs and Steel.