The answer to this is given on two levels. First, there are immediate causes that allowed the Europeans to be more successful than the Native Americans. Second, there are ultimate causes that allowed the immediate causes to come about.
The ultimate causes are essentially those that are referred to in the title of the book. Diamond says that the Europeans were able to conquer the Americas (and other areas) because they had “guns, germs, and steel. In other words, they were successful because they had better technology and because they carried germs that could (and did) devastate the populations of the areas to which they came.
But why did the Europeans have the guns, germs, and steel? Here, Diamond says that the answer is based in geographic luck. Diamond argues that Eurasia was the continent that was best suited for developing and diffusing agriculture. Because of this, agriculture arose there first and spread widely across that land mass rather quickly. This meant that the people of Eurasia could form civilizations earlier than anyone else could. Because they formed civilizations first, their civilizations were technologically more advanced by the time that they went out exploring and conquering.
Thus, the Europeans were able to conquer the western hemisphere because their geographical luck led them to have “guns, germs, and steel” while the Native Americans did not.