One word-stricken answer: nationalism.
(Devotion/loyalty to one's own country; patriotism)
Some thoughts. Note, literally entire libraries have been written on this topic and some of what I write will be controversial and the detail disputed by professional historians. This is literally only beginning to scratch the surface. These thoughts are not in order, other than the order I think of them.
- German people were desperate. They were dejected, demoralised, and suffering after the humiliation of Versailles and the later Great Depression. Desperate people are wont to do things that, after the fact, may seem irrational.
- The Weimar system had institutional features that made it relatively easy for a smallish band of extremists to make government by moderates difficult. This is true of both extremists on the left (various stripes of communist) and the right (the Nazis). Note how the modern German constitution has been designed to rule out this sort of thing, with thresholds for proportional representation in the Bundestag, constructive majorities needed to dismiss governments, and so on. When moderates fail, people turn to extremists in greater numbers.
- there was an undercurrent of anti-semitism in Germany and Europe that could be exploited by demagogues. The Nazis weren't starting from a blank slate. Anti-semitism in Europe is much older than that.
- many German elites were not too worried by the Nazis. They were more worried by communists and so were happy to ally with the Nazis against the communists. There was a real fear of what was pejoratively called Bolshevism in Europe at the time. The liberal democratic/conservative/social democratic paradigm was creaking and people thought we needed a new ideology to replace it. The elites didn't want revolutionary socialism, so they went for a different replacement. That replacement was fascism.
- in the short term, the Nazis were pretty successful both at military conquest and improving the material condition of ordinary Germans (ordinary Germans that were not part of oppressed groups). This meant that hitherto skeptical people were sometimes brought round to their point of view; maybe Hitler wasn't nuts after all
- Hitler was a pretty decent demagogue and orator, even if his ideas are evil. He genuinely did make people feel good about themselves and Germany. He made them feel part of a greater, valuable whole, working towards the glory of the German reich and volk (Empire and people).
- By the early 1930s, the Nazis had significant paramilitary muscle in the SA, and later the Gestapo and SS. Not hard to get people to go along with your mad schemes if the consequences of their not doing so is being brutally beaten or murdered. People are generally self-interested and want to preserve themselves. They will bite their tongues to feel safe.
There will of course be many more reasons. They are just a few that quickly come to mind.