Unrestricted submarine warfare is the practice of using submarines to attack and sink all forms of enemy shipping, whether they are military or civilian. It is most closely associated with the First World War when Germany's decision to use USW brought the US into the war and led to their defeat.
The Blockades of World War 1
In the build-up to the First World War, Germany and Britain were involved in a naval race to see how many bigger and better battleships could be created. When this war began, many expected the resulting navies to sail out and fight a great naval battle. In fact, this only ever almost happened at Jutland, and that was inconclusive. The British knew that their navy was the only part of their military who could lose the war in an afternoon and decided not to use it in a massive battle but to blockade all the shipping routes to Germany and try and starve their enemy into submission. To do so they seized the shipping of neutral countries and caused a lot of upset, but Britain was able to soothe ruffled feathers and come to agreements with these neutral countries. Of course, Britain had the advantage, as it was between Germany and the Atlantic shipping routes, so US purchases were effectively cut off.
Germany also decided to blockade Britain, but not only did they cause upset they caused their own destruction. Basically, the German above sea fleet was restricted to cat and mouse operations, but their submarines were told to go out and blockade the British by stopping any Atlantic trade reaching them. Unfortunately, there was one problem: the Germans had bigger and better submarines than the British, who were backward in understanding their potential, but a submarine can't easily board and sail off a vessel like the British ships were doing. The Germans thus began sinking the ships coming to Britain: enemy, neutral, civilian alike. Unrestricted submarine warfare, because there were no restrictions on who to sink. Sailors were dying, and theoretically neutral nations like the US were livid.
In the face of opposition from the neutrals (like the US who threatened to join the war), and demands from German politicians for the submarines to be brought under control, the Germans changed tactics.
Unrestricted Submarine Warfare
In early 1917, Germany still hadn't won the war and there was a stalemate on the battlefields of Western Europe. But Germany knew they were out producing the allies when it came to submarines and were still having success with their more careful policy. High command wondered: if we began unrestricted Submarine warfare again, could our blockade force Britain to surrender before the US was able to declare war and get their troops over the seas? It was an incredibly risky plan, but German hawks believed they could starve Britain out in six months, and the US wouldn't make it in time. Ludendorff, practical ruler of Germany, made the decision, and in February 1917 unrestricted submarine warfare began.
At first, it was devastating, and as supplies in Britain dwindled the head of the British Navy told his government they could not survive. But then two things happened. The British began using the convoy system, a tactic used in Napoleonic times but adopted now to group traveling ships into tough groups, and the US entered the war. The convoys caused losses to reduce, German submarine losses increased, and the specter of US troops finally broke the German will to continue after their last throw of the dice in early 1918 (a move which occurred as the Germans tried a last land tactic before the US arrived in force). Germany had to surrender; Versailles followed.
What should we make of unrestricted submarine warfare? This hinges on what you believe would have happened on the Western Front had the US not committed soldiers to it. On the one hand, by the successful allied attacks of 1918 US troops hadn't arrived in their mega millions. But on the other, it took the news that the US was coming to keep the Western allies functioning in 1917. If you had to pin it on one thing only, unrestricted submarine warfare lost Germany the war in the west, and so the whole war.