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.
history.stackexchange.com/users/1979/sds
Unlike Soviet ground forces the fleet was well prepared at the beginning of German invasion and did not panic or wait for orders.
For example as early as August 1941 Baltic fleet air force bombed Berlin from the island Ezel.
In 1941 Baltic fleet placed 12047 mines.
In 1943 the Finns together with the Germans successfully placed a net across the Gulf of Finland which Soviet submarines could not penetrate.
The operations of the Baltic fleet became confined to the Gulf.
Nevertheless the fleet played a serious role during the blockade of Leningrad and associated operations.
For instance they supported the offensive north of Leningrad with about 200 high-caliber guns.
The fleet also set up some fleet units on the lakes surrounding Leningrad, the Chud, Ladoga, Onega and Ilmen lakes.
In 1944 Finland started to remove the barrier net, increasing the possibilities for Soviet fleet.
Overall they sunk 280 enemy warships and 624 transports, including 2 pre-dreadnought battleships, 3 cruisers, 16 destroyers, and 16 submarines.
The Fleet executed 24 landing operations and 158,000 aerial sorties.
100,000 Baltic fleet personnel were awarded decorations and 137 became Heroes of the Soviet Union.
The Black Sea Fleet also was not caught by surprise; on the night of the June 22 German attack on the USSR they successfully defended against a German surprise air strike.
Throughout the war the Black Sea Fleet made 13 landings, sank 508 enemy ships, and transported 2 million passengers and 8 million tonnes of freight.
The Northern Fleet during the war sank over 200 enemy warships and 400 transports and destroyed over 1300 planes.
The Pacific Fleet mostly did not participate in the war until the 1945 war against Japan.
Many of its personnel did participate in the fight against Germany as members of other units.
Source http://militera.lib.ru/enc/0/djvu/enc_vov1985.djvu
history.stackexchange.com/users/466/Anixx
Baltic fleet
The fast German advance up the Baltic coast pushed the Soviet fleet back to bases in the gulf of Finland (Leningrad and Kronstadt).
From here their operations were severely limited by German and Finnish mines.
See the wikipedia page .
Here is a description of mine-laying activity in gratuitous detail .
Mine were layed by Germany, their co-belligerent Finland, as well as by Sweden .
The Baltic fleet did participate in the Siege of Leningrad , but it looks like their main contribution was in aviation.
The Russian submarines in the Baltic appear to have been disruptive, but weren't very effective and did not present a substantial threat .
Black Sea
Mostly inaccessible to the Germans.
As with the Baltic, their western bases were quickly taken by German land force.
The Russian navy had a huge surface fleet advantage, against the Romanian and Bulgarian navies, but this was completely nullified by German air superiority.
In this case the German land advance took all major Soviet shipyards, leaving the fleet based in Georgia with inadequate repair facilities, hindering their operational capabilities .
They were able to give some support to, and helped to evacuate, coastal cities.
Other
The Northern fleet was involved in protexting the Arctic Convoys , and supplied naval infantry forces to the Petsamo–Kirkenes Offensive against German forces in northern Finland and Norway.
The Pacific fleet participated in the Soviet invasion of Manchuria .
The Caspian
Flotilla was involved in supplying Stalingrad (via the Volga, which flows into the Caspian) as well as supplying other fighting in the Caucasuses.
history.stackexchange.com/users/1633/Nathan Cooper
The Soviet navy played an auxiliary role throughout the entirety of the Second World War.
The Baltic fleet was mainly locked in by German and Finnish mines, while the Black Sea fleet mainly participated in evacuation operations (Odessa and Sevastopol) and after the Germans retreated in 1943, attempted to gain control from German and Romanian forces.
The Navy also participated in numerous landing operations in the Black Sea (Malaia Zemlia) for which Tsezar Kunikov is famous, and Brezhnev, who took credit he didn't deserve.
Furthermore, Soviet Naval Infantry participated in numerous battles once their ships were disabled or there was a need for manpower.
From Leningrad, to Odessa, Stalingrad, Sevastopol, Novorossiisk, and 'special forces' operations (mainly conducted by naval recon troops), Soviet navy personnel made up a significant and important part of many Red Army operations.
The Germans nicknamed them 'The Black Death'.
history.stackexchange.com/users/2526/Kunikov
the soviet fleet did assist on the arctic convoys as mentionedin a post.it was also a soviet submarine that sank a german hospital ship willhiem gustloff that was acting as a evacuation ship as the russians advanced on the eastern front.
wasn't the only timea hospital ship was attacked.
a dutch and australian hospital shipswere attacked in the pacific by the imperial japanese navyin 1942
history.stackexchange.com/users/18980/user18980
In the Black sea there was also an Italian naval group of small ships.
Ans the germans managed to send a group off small speedboats using the Danube river to reach the Black sea.
history.stackexchange.com/users/13508/Bly Jean
Most books about WWII speak of the naval battles of Allied and Axis powers during the war, but none about the Soviet Navy. The Soviets had an active fleet at the time - why did it not engage the Germans at sea?
What was the role of the Soviet Navy during WWII?
history.stackexchange.com
<world-war-two><nazi-germany><soviet-union><naval><ww2-european-theater>
history.stackexchange.com/questions/6116
history.stackexchange.com/users/1681/The Byzantine
The Soviet navy had a role but it was relatively minor and did not present a substantial threat. They had a huge surface fleet advantage but this was wiped out by German air superiority. Whilst the Soviet Navy's role in WWII was smaller than that of the Soviet infantry or other Allied navies, the various fleets did play a significant role in delivering supplies to other Soviet forces, protecting convoys and carrying out numerous landing operations. The Baltic fleet was severely restricted owing to the Germans and Fins placing mines and a net across the Gulf of Finland, but despite this, the Soviet Navy was still responsible for the sinking of hundreds of enemy warships, transports and planes. On top of this, where deemed necessary, navy personnel were also provided as support for the infantry and other operations.
The Soviet Navy's role in WWII was much smaller than that of the Soviet Army or the Navy's of the Western Allies. Their strategy was directed towards preventing the enemy from using the sea in the conflict. The different Soviet fleets were involved in WWII to different extents but between them sunk thousands of enemy ships, transports and plans. The Baltic fleet alone placed over 12,000 mines. Although Russian submarines appear to have been disruptive, the Soviet navy does not seem to have been seen as a huge threat. Any advantages they may have had were nullified by Germany superiority in the air. German and Finnish activities in the gulf of Finland significantly restricted the operations of the Soviet Baltic fleet. This include the placing of mines and, in particular, a net placed across the Gulf which Soviet submarines were unable to penetrate. Other German activities, such as the capturing of Soviet shipyards, also had a significant impact on Soviet naval operations. The Soviet Pacific fleet did not participate until the war with Japan in 1945. The Soviet Navy played a significant part in supporting other land and air operations. They provided manpower for the Soviet infantry and participated in numerous landing operations, as well as delivering supplies to other Soviet forces. The Soviet navy was involved in protecting Arctic convoys and delivering other supplies to various Soviet forces.