Stalinism is the very essence of totalitarianism, as it consisted of control of every element of society. There was no limits to the power of the Soviet Government under Joseph Stalin, while at the same time he was proclaimed a great leader, so much so that after his death, his body was specially embalmed and placed in a mausoleum for permanent public viewing beside the body of Vladimir Lenin. Paranoid and scheming, Stalin knew no limitations to his power, and often had individuals arrested on suspicion of the slightest offense. He forced peasant farms to be collectivized into large state farms, the result of which was that many peasants died of starvation. While the Soviet people suffered, Stalin insisted that he was building a true Utopian socialist state. Even culture fell victim to politics, as writers and authors were told to glorify Stalin. One, Sergei Eisenstein, found himself in trouble when his comparison to Ivan the Terrible in his famous film was a bit too close a comparison for Stalin's comfort. In a telling example of Stalin's control of the society, a group of people watching a mime on the streets of Moscow were carried away and shot by the secret police because they laughed at the mime's imitation of Stalin's mannerisms.
A totalitarian government is one that tries to control people in every way. It tries to control their public lives (things like economics and political actions), but it also tries to control their personal lives as much as possible.
Stalin did both of these things. He took control of economic life, forcibly collectivizing agriculture and making other people move to places where he had them start to industrialize. He took control of personal lives as much as he could. He had a vast secret police to ensure that people did not speak out against him. He tried to get rid of religion and to build a cult of personality around himself.
In these ways, Stalinism was totalitarian because it attempted to control people's entire lives.