Soviet Navy's role was negligible compared to that of either the Soviet Army or the Navies of the Western Allies. This is not surprising given the essentially continental nature of the USSR.
The other two answers give the glorified official version which inflates ridiculously the damage inflicted on the Axis. Early in the war, the Baltic fleet was locked up in Leningrad; Tributs kept sending submarines on one way missions to show that he was doing something. After the cruiser Red Ukraine was lost in 1941, the use of larger ships had to be sanctioned by Moscow. Indeed, the Northern fleet helped with the Arctic Convoys, and late in the war both Baltic and Black sea fleets were more active, but all their achievements pale compared to what the Red Army did.
PS. The Soviet Naval Strategy was heavily directed towards Sea denial (the Shipbuilding Ministry was unofficially known as "Наркомат подводных лодок" - Submarine Ministry) which is not surprising given the aforementioned continental nature of the USSR. One might find Анализ эффективности советского подводного флота в годы Второй мировой войны enlightening, especially its scathing criticism of the official historiography.