A neighbor, Marfa Ivanovna, gives Sasha a treat—a carrot. Sasha eats this while he is waiting for his Dad to show up for dinner.
We learn that Sasha's Dad sometimes does not come home until morning, because he is a member of the Soviet secret police. Their job is to root out infiltrators who are just pretending to be good Soviet citizens.
His Dad is one of the best secret policemen around. Stalin himself awarded him the "order of the Red Banner" (which seems to be totes important) (3.1).
While waiting, Sasha takes tiny bites of the carrot to make it last. He's hungry, but he knows that a Young Soviet Pioneer has to learn to repress such cravings, since they have much more important goals.
Like achieving full Communism (which is tantalizingly close) (3.2).
Once full-on Communism kicks in, there will be lots of food. Carrots galore!
In the meantime, Sasha imagines what it's like for those poor capitalist kids who have probably "never even tasted a carrot" (3.2).