What is meant by a "eurocentric" approach to history?
A Eurocentric approach to history is one that focuses on Western civilization, in particular civilization in Europe. Diamond suggests that even world histories tend to be Eurocentric, concentrating on
...histories of literate Eurasian and North African societies. Native societies [in the rest of the world]...receive only very brief treatment, mainly as concerns what happened to them very late in their history, after they were conquered and subjugated by western Europeans.
Diamond's principal concern is that this Eurocentric approach has reinforced unfounded assumptions, such as claims that Europeans developed technology first because they were culturally or racially superior to peoples around the world. A major theme in Guns, Germs, and Steel is that technological inequalities that led to Eurasian dominance of the globe ultimately stem from geographical accidents.
Source: Diamond, Guns, Germs, and Steel, 9.