Finland had been a semi-autonomous Grand Duchy of the Russian Empire since the conclusion of the Finnish War in 1809. It was ostensibly set up as a buffer state between the Kingdom of Sweden and Russia to protect the Russian capital of Leningrad; the reason for why all this was done now instead of earlier is tied up in the complications of the Napoleonic Wars. The Russian Empire, obviously, never intended to lose Finland and put a new foreign border so close to its capital; unfortunately, that is exactly what happened. While the Soviet Union, as the successor state to the Russian Empire, wished to regain territory it lost through revolution and civil war, there were also several other factors in play.

With the turmoil of the Russian Revolution in 1917, Finland quickly seized the opportunity to declare independence, which the Bolshevik government recognized because they were busy dealing with the start of the Russian Civil War. Finland, meanwhile, had its own fracas between Red and White factions, which the Whites would win with foreign aid, mostly from Germany. Pro- and anti-communist factions would cross the Soviet-Finnish border through the 1920s in attempts to restart their respective failed movements in the neighboring countries (namely, the East Karelia uprising in the Soviet Union and the Pork mutiny in Finland). Finland remained in a state of political tumult through the 1930s, with a brief attempted coup by the fascist Lapua Movement in 1932. What this all boils down to is this: the USSR saw the capitalist societies on its borders as a threat to its security, especially the growth of a strongly nationalist Finland.

Furthermore, Finland's established border was just 32 kilometers from Leningrad. While Leningrad was no longer the capital, it was still one of the major cities of the USSR and was also the base of the Soviet Baltic Fleet. Thus, the threat was dual: there was the military threat of a Finnish invasion or restriction of the Baltic Fleet and the political threat of a successful capitalist society so close to the Soviet borders. These formed the basis for the internal Soviet justification more than simply wanting to regain lost territory.

Sources:

Manninen, Ohto. (1999). Neuvostoliiton tavoitteet ennen talvisotaa ja sen aikana [Soviet objectives before and during the Winter War]. Talvisodan pikkujättiläinen (in Finnish).

Trotter, William R. (2002) [1991]. The Winter War: The Russo–Finnish War of 1939–40 (5th ed.). Aurum Press.

Vehviläinen, Olli. (2002). Finland in the Second World War: Between Germany and Russia. New York: Palgrave.