Diamond talks about north-south and east-west axes because they have a great impact on how much diffusion of plants there can be in any given area of the world.
If an area of the world is like the Americas, its long axis runs north to south. That means that it is longer north to south than it is east to west. Eurasia is the opposite because it is longer east to west than it is north to south. It is easier for plants to diffuse along an east-west axis. This is because climate does not change east to west (outside of factors like elevation and distance from an ocean) the way it does from north to south.
This is important because a society that developed agriculture could diffuse its domesticated plants along an east-west axis to other cultures. That means that civilizations could grow and could exchange new plants with one another. In a place with a long north-south axis, this could not occur.
This is one major reason why Eurasia was so much better suited to creating major civilizations than places like Africa and the Americas were.