That's a nuclear submarine of the Russian Navy. According to translations in Russia Today, the fishermen released a stream of curse words when they realized that a nuclear submarine was so close to them, and one of them asks the other to check out how badly his hands are shaking.
YouTube user Vlad Wild played it cool when he uploaded the video, though. He titled it "Nothing unusual, just submarine." Check it out below:
Submarines work using stealth, so it's rare to see them in the wild. These two men were extremely lucky to be able to see the boat in action.