Pretty much everybody knew "about" concentration camps since they were not a secret and were often located near big cities, like Dachau near Munich and Buchenwald near Weimar. They were freely mentioned by the Nazi propaganda as rehabilitation facilities.

Now, the extent of the knowledge about the actual goings-on in the camps is another thing. In the early days of Dachau there were a few curious Germans who wanted to take a peek and they were basically told that if they were that much curious, they might as well want to spend some time there... (see Wachsmann, KL). Certainly, the rumors still spread (even if spreading such rumors was a criminal offense). Moreover, the first wave of the inmates in 1933 was largely released and they could spread some info, though they had to sign a pledge not to. Some were reserved about their experiences, with some things were more obvious, like an employee who came back from a camp without fingernails or toenails (see What we knew, p. 354).

Quite a few Germans assumed the camps were for real criminals and delinquents.

If you look at the liberation videos of the locals being led around the camps, they do seem to exhibit a genuine shock.

(Here I don't touch upon the knowledge of the extermination camps, none of which were inside the "old" Germany and must not be confused with "normal" concentration camps).