I think back to the book Night by Elie Wiesel. The Jews of Sighet were warned by a villager who had been taken away with a group of others, shot and left for dead, and then escaped. He tried to warn them, but what he told them of what he had seen of the Holocaust was too horrific to be believed. Also, some might think, "If I don't acknowledge it, it won't be true."

I think that Hitler was able to spin the Holocaust in a way that most Germans saw nothing wrong with what was going on. I am not sure the rest of the world even understood what was actually going on until it was to late to do anything about it.

The Jews and other victims of the concentration camps were victims of apathy and fear.  The public accepted each stipulation (wearing a star, not being able to go to work or own businesses, not leaving their homes, relocation to ghettos, etc.) as "no big deal" until they realized just what a big deal it was.  By then, the hold of the SS on Germany was so strong that everyone was either in denial or in such deep paralyzing fear that no one acted.

The Jews themselves felt it was better to stick it out than to risk rebellion.  They were outnumbered, unarmed, and were underfed and weak. 

There are rebellions recorded from the Jews, and there are other groups--even within Hitler's  inner circle--who attempted to help the Jews and others in the camps. 

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.

Put simply, by the time that the Holocaust (the actual killings) got started, there was nothing anyone could do other than to try to win the war and rescue the Jews that way.

The actual killing of Jews on any sort of a large scale did not happen until after Germany invaded the Soviet Union in June of 1941.  By that time, of course, the war in Europe had been going for more than a year.  There was no way that anyone outside of Germany could do anything about the killings even if they were aware of them.

Therefore, it was nearly impossible for anyone to do anything to save the Jews by the time the Holocaust had begun.