Hitler came to power in 1933 and established the Third Reich, which was a totalitarian system. The government wanted to control every aspect of life. Totalitarian architecture tries to dominate, subjugate and control society.
Most regimes, especially ones that have just taken power, want to stamp their authority on the places they rule. The most visible way of doing that is by constructing buildings and monuments. Architecture can be used to symbolise their power, but it is more than symbolism. Architecture is perhaps the only art form that has a physical impact on society - it restructures society and forces people to live a certain way.
The aims of Nazi architecture were to establish Hitler's authority and to convey Nazi beliefs. In particular, it celebrated German national identity and promoted the idea of the Aryan Race, which was supposedly made up of racially superior people with blond hair and blue eyes.
There was no official style of the Third Reich, but most Nazi architecture emulated the Classical style of the Romans. Hitler was an admirer of Imperial Rome. He was trying to create a new empire. The style was usually enlarged and exaggerated, sometimes with ludicrous results. Albert Speer became Hitler's favorite architect. Speer's style was a severe, simplified Classicism, which is often known as stripped Classicism. Stripped Classicism was popular in the 1930s and was actually used outside of Germany.
Speer designed the Zeppelinfield Arena at Nuremberg (1934) [Fig. 1]. This was built on an enormous scale and was capable of holding two hundred and forty thousand people. This was used for the colossal Nazi rallies, in which architecture and political dogma fused in a terrifying ceremony. Again, it's a severe form of Classicism, purged of decoration, leaving only the basic muscular style. Speer created the famous balcony from which Hitler gave speeches.

Fig. 1 Zeppelinfield Arena, Nuremberg
This illustrates the vacuous mentality of the regime. The arena was an empty stage set for Nazi pageantry. Hitler wanted architecture with an instant monumentality, so this was built very quickly. Albert Speer lifted elements from various historical sources and diluted them, making them larger, simpler and more severe and monumental. These buildings were characterised by regimental repetition, which was a metaphor for an ordered society.
The neo-classical style was primarily used for official buildings. Speer designed the new Reich Chancellery (1938), which had an incredibly long corridor leading to Hitler's office, lined with red marble [Fig. 2[. The overwhelming length, rich materials and pompous regimentation were meant to intimidate visiting statesmen. This building had a bunker underneath it, which is where Hitler hid for the last weeks of the war and where he committed suicide in 1945.

Fig. 2 Reich Chancellery, Berlin
Hitler began to remodel Berlin because wanted to create a grandiose imperial city. The Volkshalle (People's Hall) was a huge monumental building planned by Hitler, but never built [Fig. 3]. It would have been impossible. Visually it was to have been the architectural centrepiece of Berlin as the new world capital. It was based on the Roman Pantheon, with this great dome, but it was so vast that the cupola would have been bigger than the dome of St. Peter's Basilica in Rome.

Fig. 3 Model of the Volkshalle
Speer did not only design physical buildings. He also orchestrated the Nazi rallies we mentioned earlier. His greatest feat of showmanship was to point 1000 searchlights at the sky, forming the so-called Cathedral of Light [Fig. 4]. They were actually anti-aircraft searchlights, which hints at the violence and the military threat lying just under the surface of the Third Reich. The ordered columns of light are reminiscent of the neo-classical architecture he used elsewhere; they create a sort of spectral architecture, an ethereal architecture made of light.

Fig. 4 Cathedral of Light