Submarines played an enormous and decisive role at the Battle of Jutland - not through their actions, but through the fear of them that was firmly planted in Admiral Jellicoe's mind. As /u/thefourthmaninaboat points out, submarines were far too slow to operate with the battle fleets. Jellicoe of course knew this fact, and he also knew that the general German strategy would be to attempt to whittle down the numerical advantage possessed by the British by luring them into situations where isolated units could be outnumbered and destroyed. He assumed that part of this strategy would involve attempts to lure British ships into minefields or regions where German submarines were waiting (he was reinforced in this fear by the loss of the dreadnought Audacious to a German mine early in the war). He therefore determined that he would never follow the obvious course offered by the German fleet during a withdrawal (i.e. he would not chase them directly in such a situation), and stated these intentions to the Admiralty in writing at the start of the war (and received their approval, as they understood that the preservation of the Grand Fleet was necessary for the survival of the British Empire).

At the most critical moment of the Battle of Jutland - when the two main battle fleets first encountered each other - Scheer, recognizing the bad situation he was in, executed an abrupt about-face maneuver and reversed direction. Jellicoe, out of fear of submarines (and mines that he thought the German ships would be dropping behind them) - and exactly as he had said he would do - neglected to follow directly, thereby missing what was likely the best opportunity the British had to destroy the German fleet completely.

It is normally presumed that other than the morale impact, the loss of the High Seas Fleet would not have affected Germany's military position much, but I don't think think is necessarily the case. In both world wars, Germany's military industry was dependent upon high-quality iron ore from Sweden. In WWII, Germany's control of Norway as well as air power meant Britain could not penetrate the Baltic and interdict the surface traffic to and from Sweden; in WWI only the High Seas Fleet kept the Royal Navy out of the Baltic. If Jellicoe had shattered the High Seas Fleet at Jutland, it would likely have ended the war. So in a sense, the role submarines played at Jutland helped prolong the war by two years.

Sources:
Castles of Steel, Robert K. Massie
Battleship, Peter Padfield
The Great War at Sea, Richard Hough
Dreadnought, Richard Hough