Short answer: They tried. It didn't work.
Long answer: First, a bit of background. While anti-submarine warfare was in its infancy in WWI, so were the submarines themselves.
It's a common mistake to imagine early submarines as being only incrementally different in capabilities from modern attack subs, but there are fundamental differences. For one, modern attack submarines are major warships: a Virginia-class submarine costs about twice as much to build as an Arleigh Burke class guided-missile destroyer (the US Navy's main current surface warship, more like a traditional heavy cruiser in operational role than the "destroyer" label suggests) and mounts similar primary weapons (launch cells and tubes capable of firing Tomahawk cruise missiles and Harpoon anti-ship missiles) albeit fewer in number (12 vertical cells and 4 tubes on the Virginas with a total of up to 60 missiles including reloads vs 96 vertical cells and no additional reloads on the Arleigh Burkes). The other huge difference, arguably the more important here, is that modern subs are designed to operate almost entirely underwater for extended periods of time.
Neither of these things were close to true for WWI-era submarines. They were very light warships, barely large enough to be seaworthy while carrying a useful armament (about 5-10% the size of a modern attack sub), and were designed to operate mostly on the surface. They could dive of course, that being the defining feature of submarines, but only for short periods to evade or ambush an enemy ship. They were slow when surfaced and even slower underwater, and underwater they were entirely dependent on stores air for breathing and lead-acid batteries for power and propulsion: "snorkels" allowing running diesel motors while submerged at shallow depth ss weren't deployed until well into World War II, air-independent propulsion (e.g. using hydrogen peroxide as an oxidizer to allow running engines when submerged too deep for snorkeling) only reached the full-scale prototype phase by 1945, and were little more than theoretical possibilities 1914-1918. Nuclear propulsion, of course, wasn't developed until the 1950s. You can see this distinction reflected in ship hull design: modern subs have cylindrical hulls with blunt rounded noses and no external armament, for minimum drag while submerged, while older subs had pointed prows and flat decks like a surface warship and generally mounted a light anti-ship cannon (and later anti-aircraft guns) on the deck for fighting on the surface.
These differences reflected and informed a fundamental difference in operational role. A modern attack sub has two major roles. The first is to track and engage enemy submarines, especially ballistic missile submarines, in a way that other ASW platforms can't (both the ability to follow them closely while deeply submerged and the ability to try to track them while remaining undetected). The second is to act as a compliment to the surface fleet, performing similar kinds of missions as a major surface warship (engaging enemy warships, missile strikes on land targets, etc) while trading some offensive capability for stealth and survivability due to the ability to operate submerged.
WWI subs, on the other hand were intended to operate from ambush only, using stealth to get in range to attack larger and faster ships with their very limited armament (deck guns against unarmed merchant ships or military transports, or torpedoes against warships). The first few generations of subs were intended for coastal defense only, being little more than submersible variants of torpedo boats. By WWI, submarine fleets had had their missions and capabilities extended to also include commerce raiding and ambushing warships on the high seas. In many respects, you could think of a WWI-vintage submarine as a mobile minefield rather than as a proper warship.
The pre-war German naval war plans against Britain relied on the assumption the Britain would attempt a traditional close blockade, stationing squadrons of warships just out of range of shore guns of major German ports to control the approaches to intercept ships trying to enter or leave. Germany would counter this by laying minefield and by using submarines and torpedo boats to attack vulnerable ships, whittling down the strength of the Royal Navy until it was weak enough for the main German battle fleet to sortie and defeat them. Unfortunately for the German Navy, the British declined to cooperate with their plans. A few years before the outbreak of war, the British First Sea Lord Admiral Jackie Fisher foresaw the risk of losing major warships to German coastal defenses and revised the plans to a Distant Blockade strategy instead: the main British battle fleet would concentrate in defensible anchorages far from the German shore (Rosyth, in Scotland, and Scapa Flow, in the Orkney Islands off the north of Scotland) while the blockade would be enforced by expendible light warships (cruisers and destroyers) and obsolete ships drawn from the mothballed reserve fleet, patrolling the English Channel and the North Sea. If the Germans sent a major fleet to try to break the blockade, then the British battle fleet would sortie and intercept them.
Even so, the German attritional strategy did get some notable successes in 1914: the new advanced British Battleship HMS Audacious sank after hitting a German mine laid off the coast of Ireland, and three British Armoured Cruisers (major warships when they were built c. 1900, but by then semi-obsolete ships drawn from the reserve fleet for patrol duty) were ambushed and sunk by a German submarine off the Dutch coast.
Later in the war, the German Navy switched to a strategy of using coastal raids (sending Battlecruisers to shell under-defended towns and cities on the British coast) to lure elements of the British battle fleet into sortieing so it could be ambushed and defeated in detail. Submarines often formed part of the planned ambush: the Germans would deploy a line of ten submarines across the expected course of the British fleet prior to the raid. They attempted this several times, most notably at the raid that lead to the Battle of Jutland in 1916. It didn't work: the British had some idea what was planned due to intercepted and decoded radio intercepts, British anti-submarine patrols forced several of the subs out of position, two had to turn back due to mechanical problems, and the subs (with their very limited mobility and armament) didn't get any good opportunities to ambush major warships.
Towards the very end of the war, in October 1918, the German Navy planned one more attempt at this operational concept: the whole German battle fleet would leave port and raid shipping and shore targets in the Thames Estuary and the vital supply ports on the French/Belgian side of the English Channel, while the (now much larger) German submarine fleet would be deployed in multiple ambush lines between the Rosyth and Scapa Flow bases and the target of the German raid. My main source for this (Massie) thinks the plan was viable, but he seems to be in the minority in this view. More importantly, most of the sailor in the German fleet disagreed violently with the plan, viewing it as a futile and suicidal act of defiance to try to stave off inevitable defeat. The sailors mutinied, kicking off what would become known as the German Revolution, which would lead to the German Emperor's abdication and the establishment of the Weimar Republic. The German Revolution has also been blamed by some for Germany's defeat in WWI (the "stab in the back legend"), but the overwhelming consensus of modern historians is that the German military had already been decisively defeated prior to the Kiel Mutiny.
Sources:
Modern warships basic info: Navy.mil fact files for public information on missions and capabilities of Arleigh Burkes and Virginias. Some additional details from Wikipedia where they were missing or unclear on the navy.mil sources.
General background on modern warship operational roles: "How to Make War" by James Dunnigan
Pre-ww1 ship design and naval planning: "Dreadnought" by Robert K Massie
WW1 naval operations and the German Revolution: "Castles of Steel" by Robert K Massie and "No Man's Land" by John Toland.
"Stab in the back" Legend: "The Coming of the Third Reich" by Richard J. Evans and "Hitler's Empire" by Mark Mazower
Because of the armament of the submarines, their tactical use, and strategical decisions.
Armament and tactical use:
Strategical decisions: After the Battle of Skagerrak (1916) the Imperial Navy command learned that the British Navy was superior, and it was suicidal to launch a larger attack on it to break the blockade. Besides, German navy soldiers in the lower ranks very often had a working class background and many were pro-communist, they played a large role in the November revolution and communist uprisings afterwards. It may have been decided that they would not be sent out to suicidal missions to avoid mutinies.
While the other answers to this post have covered the possibility of Germany using its submarines to attack the ships that made up the British blockade, this was not the only way to break the blockade. Large cargo submarines could provide a way to evade the blockade and carry cargoes to and from Germany. Two such submarines were completed, with six built but converted into long-range 'cruiser' submarines.
The two that were completed were the Deutschland and the Bremen. They were built by a private company, a subsidiary of the main German shipping line (the North German Lloyd line). Between them, they made three voyages as merchants. Deutschland made the first trip, leaving Kiel on the 23rd June 1916 with a cargo of precious stones and dyes. She successfully reached Baltimore on the 9th of July. She would depart for Germany in August, with a cargo of strategic materials including tin, nickel and rubber. Bremen made her maiden voyage to America in August, but never arrived. She vanished somewhere in the North Sea or Atlantic. It's possible that she was accidentally rammed by one of the British auxiliary cruisers of the 10th Cruiser Squadron, which enforced the blockade of Germany. Two of them, the Alsatian and Mantua, reported collisions with underwater objects at about the time Bremen would have been passing by. There are a lot of other possible causes for a WWI-era submarine to sink, though; they were not the safest things in existence. Deutschland made another trip to America in November, again carrying valuable cargoes of chemicals on the way out and strategic materials on the way back. She would not have a chance to make a third journey. The rise of unrestricted submarine warfare and America's ensuing entry into the war led to her being requisitioned by the navy. Germany needed more submarines and with America in the war, there was nowhere practical for her to go. She made several war patrols under her new guise, sinking a total of 43 ships. Surviving the war, she was seized by the Royal Navy under the terms of the armistice, and displayed around Britain as a trophy.
The cargo submarines were more of a novelty than a practical solution to the blockade. They had a cargo capacity of 780 tons. However, 250 of this was carried in flooded spaces outside the pressure hull. This meant that they could only really carry small, valuable cargoes - chemicals or precious stones on the way out, and rubber and strategic metals on the way back. Germany needed more than these; it needed hundreds of thousands of tons of food, fertilizers, fuel and animal feed to avoid the deprivation it suffered in 1917-18. The submarines could not carry these efficiently, especially since these were too perishable to carry outside of the pressure hull, cutting their carrying capacity by a third. However, they could be imported in significant quantities through Germany's neutral neighbours, either by buying directly from them or by importing cargoes to their ports and then overland. This route was only cut off by the British after Deutschland had been requisitioned by the German Navy. As the loss of Bremen shows, the use of submarines was not a foolproof method of evading the blockade, as accidents or enemy action could still sink them. Finally, there were legal issues. While merchants of belligerent powers were allowed to trade in neutral ports, it wasn't entirely clear how submarine merchants fit into this. Given that all other submarines of the time were armed, and it wasn't clear to the Allies that Deutschland wasn't, the Allies felt she should be treated as a warship. This view was bolstered by the fact that, especially when submerged, that she was almost impossible to tell from a warship. Such ships were legitimate targets, and could be sunk on sight. The Germans, of course, held that she was a legitimate merchant vessel, and subject to prize rules. Had the Germans attempted to use cargo submarines to a greater extent, the Allies might have made a greater legal effort to have them banned from American ports or interned if they tried to enter them.