There was not just the one reason. A number of factors eroded the trust into the democratic government of the Weimar Republic.
The "Dolchstoßlegende"/“Dagger Legend“. After the WW1, an influential general framed the democratic leadership for surrendering while Germany was not yet defeated (“Stabbed in the back”). While it was true that no Allied troops had yet entered Germany, the German army was on the brink of total collapse and a few more weeks would have finished it. However, a lot of Germans didn’t want to believe that all the years of suffering had been in vain, and so clung to the conspiracy theory of traitor-democrats. This early on eroded trust in the young Weimar Republic.
The Weimer Republic never went past its infancy. The majority of Germans had been born during the time of the German Empire. While the German Empire had some democratic elements, it was also relatively authoritarian, especially during WW1. Germans did not yet have an established democratic tradition, before disaster struck.
The Great Depression. Germany was as devastated by it as any other country. As capitalism crumbled, a lot of people started to be more open to radical solutions, such as communism and fascism.
General polarization. During Weimar, both the extreme right and the extreme left increased in power and aggressiveness.
The make-up of the German voting system. Weimar was not a first-past-the-post voting system. A party that got 1% of the votes also received 1% of the seats in parliament. Parties had to build coalitions to pass laws and elect the government (E.g. Zentrum(25%)+SPD(30%)=Stable government (55%)). While a lot of Americans might now start to get jealous, this system malfunctioned badly. A plethora of micro-parties siphoned votes and required bold coalitions including multiple parties, each with its own agenda. Coalitions in Weimar were notoriously unstable, eventually rendering Germany ungovernable. The President had to pass laws with “Notstandsverordnungen” (similar to Executive Actions) because Parliament was unable to do so. So when Hitler and communists ranted against democracy and advertised authoritarian rule, people had a hard time coming up with a counter-example. Modern Germany has the rule that any party that fails to collect at least 5% of the vote just is excluded from Parliament, in order to prevent another Weimar-like fracturing. Also, a government cannot be dismissed unless a new government is voted-for in its place, thus preventing a leadership-crisis.
Now, we can finally turn to Hitler himself.
Firstly, keep in mind that Germans were unable to predict the future.
Hitler’s party, the NSDAP, means “National Socialist German Workers Party”. The Nazis were not socialists (despite their name), but even so they had the option to connect to the ordinary man on the street. Hitler himself was unemployed during the Great Depression, living in a men’s shelter. Many people could relate to that (Stuff like “He is one of us”).
The NSDAP catered to the military. Hitler and many other high-ranking Nazis once had been soldiers – just like a whole lot of Germans following WW1. Many Nazis wore uniforms, to pronounce this. In addition, the entire former German Empire was quite militarized, e.g. with children wearing fancy parade-uniforms to show their patriotism. This was fertile soil for a party with paramilitary ambitions.
The Red Menace. Many Germans were afraid of the rise of communism. The Weimar Republic was started twice, once as a communist republic, once as a “capitalist” one (I know these are anachronistic Cold War Terms, but people know them). The latter won, but communism remained a strong current in Weimar. Hitler was an anti-communist-hardliner, and many people hoped that he would preserve the German heritage against a progressive communist take-over.
Xenophobia. Poverty (Great Depression) breeds resentment and the need for scapegoats. I don’t think I have to explain how the Nazis were xenophobic.
The Treaty of Versaille. But not as simply as some people claim. In and of itself it was not horribly bad, but it rubbed many Germans the wrong way and its bad reputation offered a good staging-ground for people who wanted to “restore Germany’s honor”.
Coercion. The NSDAP had a special group of paramilitary thugs (the SA, Storm Department) who could bully people who were too outspoken against national-socialism.
Source: German Highschool. We talked about this topic a lot. Also: German newspapers, German history books, German museums, …
I read a response to this question a few weeks ago that really struck me.
Following the defeat of the central powers, the Treaty of Versailles was struck which outlined peace terms and conditions. The conditions were fairly harsh, forcing Germany to cede provinces (many of which were culturally dominated by Germans), limit their military powers, pay enormous reparation payments, and "humiliatingly" concede that Germany was responsible for causing the war in the first place. (https://www.ushmm.org/wlc/en/article.php?ModuleId=10007428) As you can imagine, Germany began to erode. If your country was impoverished, embarrassed, and starving, it would not be surprising for you to admire a political figure that calls for the empowerment and unity of the people against those that imposed such harsh demands upon them. Hope this helps :)