It's a complicated question with more than one answer. The Holocaust happened in areas ruled by the Nazi Party, including most of Europe at one point. This was totalitarian rule at its purest, and the Nazis did what they wanted to. To those living within the Third Reich at the time, they had to seem unstoppable, given that they had the power to imprison or execute anyone who challenged them. The Gestapo and the SS who largely orchestrated the Holocaust were terrifying in terms of their power and the ways in which they used it.
Another answer is that many people, Germans especially, did not want to see what was happening. They were told Jews were being resettled, and while this didn't really make sense, and some of the camps were in Germany, it would be a pretty horrible truth to behold that your own country, your own people were committing genocide.
A third factor in why people did nothing (but not the last reason, there are many more) centered around people's prejudice and racism at the time. Jews were easy targets, they were unpopular all over the world (even in the US) and anti-Semitism had been common in Europe for centuries. So there were undoubtedly some, although they would deny it later, who wanted the Holocaust to happen, and even may have benefited from it directly in terms of property or wealth.
All of this being said, there were thousands of individuals, and some whole countries who stood up and tried to help. See the link below for some good examples.