It boils down to a few basic ideas
1: Native american's had no real concept of quarantine. If someone was sick, the extended family would take care of them. In turn the extend family would become infected, and infect the rest of the village/tribe as they travelled.
2: Europeans lived in cities with much greater population densities. Their immune systems were much more accustomed to dealing with a large variety of infectious agents. Whereas the native americans live is small homogenous villages. With very little exposure to outside influences, other than other tribes/villages.
Here's the wikipedia page, which actually goes into more depth:
A personal pet peeve of mine is that Alfred Crosby wrote about this stuff in the 1970s (The Columbian Exchange) and the 1980s (Ecological Imperialism) but Diamond gets all the credit for it because he successfully repackaged it for more popular audiences, without adding much.