From a historical point of view, I would say that the public confessions and executions that follow represent the Stalinist purges. Stalin used the purges as a way to consolidate his own control and the power he held over the people. He used them as a way to eliminate dissent and silence any potential criticisms of he and his governing. In Orwell's work, Napoleon uses them in much the same way. He is concerned with identifying anyone who spoke out or acted against him. Napoleon is driven to keep them silent, and to ensure that there is total devotion and obedience to what he says and does. In bringing out the public confessions and executions, Napoleon is able to make a statement about how things will function on the farm. This represents his own desire to consolidate control at all costs, a line drawn that clearly demarcates where order and structure lie on the farm. Napoleon's actions in chapter seven demonstrate and represents his utter brutality and the fact that he is not afraid to doing what he has to do in order to ensure allegiance and absolute conformity to he and his reign.
In Chapter Seven, a number of the animals make public criminal confessions and are executed by Napoleon's dogs. This bloody scene is important for a number of reasons. First of all, it represents the completion of Napoleon's transformation into a totalitarian dictator. These executions demonstrate the extent of Napoleon's power and authority: the animals are so terrified of Napoleon that they feel compelled to confess to criminal activity, no matter how trivial that crime might be. In one case, a sheep admits to urinating in a drinking pool, an extremely minor offense for which this animal loses his life.
Secondly, by depicting these executions, Orwell creates a strong parallel between fiction and real events that took place in Soviet Russia. Stalin (represented here by Napoleon) used show trials and executions to remove the people that he believed posed a threat to his position. By recreating these trials in the novel, Orwell shows just how brutal Stalin really was and, in a more general sense, makes it clear that life in Soviet Russia was far worse for the typical person than it had ever been before. This sentiment is echoed in Animal Farm: the animals are in a far more miserable and oppressed position under Napoleon than they ever were under Mr. Jones.