"The degeneration of Weimar Germany's democracy into the Nazi state". Essentially refers to the idea "nazifying" of German life. This goal was accomplished by the SS working at the local level, and the Nazi leadership working at the national level to co-ordinate all aspects of German cultural, educational, and social life.

What did it Entail?

Centralization of Power
"Federal States" - Regional parliaments dissolved and reformed, allowing them to be tools of the Nazi agenda (March 1933)
"Reichstatthalter" - "Reich Governors" who were members of the Nazi party (April 1933)
Regional Parliaments Closed - Federal governments were put under control of the Ministry of the Interior (January 1934)
These measures effectively ended the federal principle of government in Germany.

Trade Unions Banned
In order to get rid of the perceived threat that German organized labor posed to Nazism, SA and SS occupied trade union headquarters, confiscated their funds and and arrested their leaders (May 1933). All trade unions were then banned, and replaced with the "German Labour Front". It became an insturment of control over its members rather than a tool for the members to use to gain rights, increase wages and better working conditions. This was pretty much the end of the organized German labor movement.

Destruction of Political Parties
After the nazis took control, most political parties had already been banned (communists) or they willingly dissolved (nationalists and catholics). In July of 1933 there was a decree which said the Nazi party was the only legal party, but at that point it was already decided anyway.