It stemmed from the desire of Stalin to exercise control of Poland following the war. Security was the foremost concern of senior Soviet leadership, and after Germany essentially used Poland as a convenient path into Russia twice in a twenty year period the Soviets decided it was essential to their security to control the territory and make sure any future invasion stopped their rather than outside Moscow.
In order to facilitate this they sought to eliminate anyone with the experience or credentials to mount an effective resistance to Soviet-backed communist control. The officers murdered at Katyn were one group, but so were academics, politicians, religious leaders and even non-Soviet backed communist groups. This also explains the reluctance of Stalin to allow the Polish government in exile any say in the postwar disposition of the country.
The Soviet Union employed similar tactics throughout eastern Europe, using the Red Army not just to kill Nazis but also anyone that may oppose the creation of a client state. Timothy Snyder's Bloodlands is an excellent, though depressing, book on the subject.
hi! Not discouraging further discussion here, but fyi, there have been a couple of interesting threads on this topic - check them out!
What was the point of the Katyn Massacre? - unfortunately featuring a now-deleted account user
Why did the Resistance movement of Poland failed to resist the overtake of URSS in 1945 ? - featuring /u/Georgy_K_Zhukov
Wasn't Russia on the "good" Allied side?
Not exactly. The Soviet Union switched sides during the war. The massacre occurred while the Soviet Union was allied with Nazi Germany.
Under the Molotov-Ribbentrop pact (August 1939), Germany and the Soviet Union agreed to partition Poland between them. Germany invaded Poland from the west, and the Soviet Union invaded from the east. The Katyn massacre took place in April and May 1940.
Background on the reasons for the Nazi-Soviet alliance: see George F. Kennan, Russia and the West under Lenin and Stalin.
In June 1941 Germany launched a surprise attack, invading the Soviet Union. After that the Soviet Union and Britain (and later the US) had a common interest in defeating Germany.
The Western democracies lacked the power to defeat Germany on their own, so they needed the alliance with the Soviet Union, even though it was a totalitarian dictatorship. (Discussed in George Kennan, American Diplomacy 1900-1950.)
In Politics Among Nations, Hans Morgenthau discusses moral restraint in international politics. He cites an incident at the Tehran conference (1943): Stalin suggested (perhaps jokingly) to Churchill and Roosevelt that future German militarism could be prevented by executing 50,000 German officers and technicians, thus decapitating the German leadership. (Churchill vehemently rejected this suggestion.)