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.