What is meant by a "Eurocentric" approach to history in Guns, Germs, and Steel?
You can answer this question by looking in the Prologue. There, Diamond clearly defines what a Eurocentric approach to history is. On page 17 in the paperback version of the book, Diamond says that a Eurocentric approach is one that includes
...a glorification of western Europeans, and an obsession with the prominence of Western Europe...
In other words, a Eurocentric approach to history is one that implies that Europeans are better and more important than everyone else in the world. It is an approach that looks at European dominance in the world and assumes that that dominance is natural and permanent. It is an approach that gives Europe too much credit and does not look at the importance of other parts of the world.