Democratic Centralism was a concept introduced by Lenin in his work "What is to be done?"(1902). In this work, Lenin argues that the success of the Social Revolution can only be secured by a Vanguard, made up of the Communist party. Or rather, Lenin argues that Marx said the above, although Marxist never did. But I digress:

Now, according to Lenin, the Vanguard-party was to be supreme and unquestionable in its authority, it was, after all, the vanguard of the revolution. So showing the public disagreements and feuds could result in the questioning of the strenght of the vanguard, and inspire reactionary forced to rebel. This meant that all disagreements and differences were kept internally in the party, hell, Lenin encouraged it, but only the party was to know about the various disagreements.

This system continued throughout the history of the USSR, untill Perestroika and Glasnost that is, with relatively little change. Also under Stalin.

While Stalin served as General-Secretary of the Communist party, there were still plenty of disagreements and differences within the party. Stalin seemingly didn't like this, and in 1936 arranged a series of show-trials to get rid of the internal opposition. Anyone who was seen as "enemies of the revolution" were killed, jailed, 'reeducated', send to Sibirian labour camps, or into exile.

But the system of Democratic Centralism continued. It was, de jure, still the Communist Party, the "Vanguard", that held all power, and not just Stalin. That the cebtral comittee of the Party was made up of 95% Stalin supporters, and 5% people who were too afraid to argue against Stalin, this gave Stalin de facto unlimited power.

Sources:

Lenin, Vladimir I; What is to be done, 1902

The Great Soviet Encyclopedia

Thurston, Robert W; Life and Terror in Stalins Russia, 1998