People place too much emphasis on Hitler's oratory skills because the idea of one guy hypnotizing everybody with speeches is a simple and appealing narrative. You can find his speeches on Youtube and they're mostly just angry shouting, maybe it's just that norms have shifted in response to him but it really doesn't seem like anything special.
To understand the real story you have to understand the broader history at the time. I started writing this comment and it just grew and grew so I apologise for the length.
Socialism in Europe
In the early 20th century, socialism was growing in popularity and labor movements were becoming more organized. Marx had predicted a simultaneous, worldwide revolution, with the working class uniting across every nation. During the Russian Revolution, countries across Europe sent troops to stop it but failed, and there was a fear that the USSR would sweep across Europe with the support of socialists in each country.
The reality was that there were major differences between the social democrats in Germany, France, and Britain compared to the Marxist-Leninist USSR, one major point of contention being WWI. Lenin argued for "revolutionary defeatism" where socialists would openly call for the defeat of their own governments and take advantage of the state's difficulties to overthrow it. Social democrats believed in gradually reforming the system and working within it, which included not making serious waves over the war, and only really criticizing it on principle, in the abstract.
In Germany, the SDP voted in favor of selling war bonds at the start of the war, indicating their willingness to go along with it. However, towards the end of the war, once it was clear that Germany would be defeated, a revolution occurred.
The German Revolution and The Spartacist Uprising
In 1918, sailors at Kiel saw the writing on the wall and mutinied, defying orders to deploy against the British navy. This happened organically, without leadership or a clear political agenda beyond being unwilling to keep fighting. But it would soon become clear that the reich had fallen and that the war was lost.
Two factions emerged that tried to steer things in different directions. One was the social democratic SDP, and the other was the communist Spartacist League, later the KPD. The Spartacists wanted to enact radical reforms and to set up a council republic similar to the Soviet system, while the SDP wanted a parliamentary system. The SDP won, and executed the Spartacist leadership, which led to an irreparable rift with the KPD.
In order to form a governing coalition in the new parliamentary system, without any chance of working with the KPD, the SDP had no choice but to ally with center-right parties. And because they had no choice, that meant the center-right parties held all the cards.
The Weimar Republic
Having lost the war, the new government had no choice but to accept the harsh terms of the Treaty of Versailles, which included ceding territory, war reparations, and demilitarization. But there was roughly a decade, the 1920's, when they were able to rebuild, recover, and make some social progress. The German film industry in particular thrived, with films like Nosferatu (1922) and Metropolis (1927) establishing Germany as the cultural center of this new medium (which would last until Hitler destroyed it, leading many talented filmmakers to flee to the US and lend their talents to Hollywood).
But then the Great Depression hit. People all around the world were struggling, and the war reparations placed an additional strain on the Germany economy. To make matters worse, the governing coalition of the SDP and center-right parties enacted austerity measures, aimed at balancing the budget instead of economy recovery, and the reduced revenues meant cutting social spending at the time it was most needed. Unemployment skyrocketed. People were desperate, and furious at the government, labelling Chancellor Brüning "The Hunger Chancellor," and the SDP lost credibility by association.
People wanted change, and the wanted an explanation for how things went wrong.
The Stabbed-in-the-Back Myth
Enter, the Nazis. The Nazis provided a simple explanation for where things went wrong. Things went wrong when Germany was defeated. Germany was defeated, because the socialists had turned traitor and betrayed it.
There were bits and pieces of truth in that narrative. Lenin had called for socialists to do that, as he did in Russia, but few in Germany had really listened to him. The SDP had fully supported the war, which caused Lenin to fiercely denounce them. There was eventually a revolution, but by the time it occurred it was already clear Germany was defeated. In that revolution, the faction that was more aligned with Lenin's ideas had been crushed.
But, by lumping both factions together in "the left," and ignoring any facts that didn't fit, they were able to weave together people's frustration with the current government with their fears and animosity towards the communists into a simple narrative that played on people's patriotism and the pain of having been defeated.
Then, they took it a step further. Because it was somewhat hard to ignore some of these inconsistencies and the fact that the two factions on the left hated each other's guts. But what if the connection was that they were both being manipulated into betraying Germany, on behalf of a sinister force behind the scenes?
Antisemitism and Nazi race theory
In mideval times, it often happened that kings wracked up tons of debt, often on pointless military adventures, and when the debts couldn't be paid, they simply blamed it on the Jews, which also conveniently let them seize their assets when they expelled them from the country (a similar approach to what the Nazis did). There was a lot of preexisting racial prejudice and stereotypes, going back centuries if not millenia. Framing things in racial terms allowed the Nazis to take advantage of existing stereotypes and prejudices, and also allowed them to present an alternative to the class-based narratives of the left.
Racial equality was a relatively new idea that was not broadly accepted, and the Nazis were able to frame the very idea of equality as another Jewish conspiracy.
How did Jews end up in control of everything if white people are the superior race? In the Nazi view, the ideal is a balance between thought and action, in line with the image of a "self-made millionaire." Some races, they claimed are inclined towards action, but not thought, and so their "natural place" is to be put to work in service to others. Jews, on the other hand, were too inclined to thought rather than action, they were uninterested in actually building anything and only interested in finding ways to take what others had built. In order to prevent white people from acting against them in a strong, decisive way, they promoted ideologies like communism, which called for racial tolerance and compassion. As the Weimar Republic had made early strides in trans healthcare, this was also called a Jewish conspiracy to weaken and soften white men.
Hitler becomes chancellor
As the economic conditions continued to decline, and as the far right grew stronger and gained more and more seats in parliament, neither the SDP nor the KPD showed any interest in reconciling. The SDP denounced the KPD and the Nazis as being equally bad and undemocratic and the KDP accused the SDP of being "the moderate wing of fascism." The SDP saw the KDP as a liability that would alienate their other coalition partners, and the KDP did not want to associate themselves with the disasterous austerity policies the SDP's coalition was enacting. Not only did they oppose each other in parliament, but they even fought each other in the streets, even as the Nazi brownshirts were pushing them both out.
Eventually, the SDP/center-right coalition no longer had enough seats, and nobody was willing to form a coalition with the Nazis or the communists, which triggered a constitutional crisis. Most parliamentary systems have rules and contingencies for if a coalition can't be formed (in part because of this), but the Weimar system lacked clear rules. Without a majority, the government simply couldn't govern, and with riots and street-fighting breaking out everywhere, there was a fear of full on revolution.
This finally brings us to the 1932 presidential election, between Adolf Hitler, Paul von Hindenburg (a center-right candidate backed by the SDP), and Ernst Thälmann of the KDP. Hindenburg won, and his chief concern was restoring stability and protecting business interests, and he appointed Hitler chancellor with those goals.
With the ongoing constitutional crisis and unclear rules, Hitler found a legal argument that essentially gave the chancellor dictatorial power. The streets already belonged to the Nazis. When the first concentration camps were built, they were for the communist KPD, and the SDP raised no objections, not realizing that they would follow not long after.