What is meant by a "eurocentric" approach to history?
The previous post was accurate. It seems that one of Diamond's fundamental driving points is to attempt to add to or modify the existing narrative of world development. In this expression, the power of the European element is undeniable. It is shown through the reality of colonization and the reality of imperialism. These elements are depicted in a Eurocentric viewpoint as examples of European glory and conquest. A moment in time where strength, calculation, and an almost divine providence allowed European expansion into different parts of the world. Diamond seeks to add to or modify this with the inclusion of the realities experienced by those who were "on the other end" of this advancement. In this light, a "Eurocentric" approach does not take into account other narratives and experiences, something that Diamond seeks to do.
I assume that you are talking about the word as it is used (p. 17 in my book) in the Prologue. This is where Diamond says that some people will argue that answering Yali's question "involves a Eurocentric approach to history." If that is the case, look a little bit further and you will see the definition of the term.
What Diamond says is that this is an approach that glorifies Europeans and is obsessed with the prominence of those people. In other words, Eurocentric history is history that is centered on and told from the point of view of Europe. It is history that tends to assume that what Europeans do is more important than what anyone else does.