The initial idea for the tanks seems to have come from Major-General Sir Ernest Swinton, who in October of 1914 first proposed:
a power-driven, bullet-proof, armed engine, capable of destroying machine guns, of crossing country and trenches, of breaking through entanglements, and of climbing earthworks.
This amazing weapon was duly designed, and the first "tanks" (so-named to convince any unscrupulous observers watching their parts being shipped that they were merely new water tanks) made their limited debut at Flers on September 15, 1916, where they met with mixed success.
Their "influence" is somewhat difficult to measure given the limitations involved in producing and deploying them in the first place. On the one hand we are confronted with the tremendous enthusiasm of pretty much everyone involved, with certain notable theorists, statesmen and generals of the time almost convinced that the tank could win the war alone; on the other hand we are confronted with the construction problems, design flaws and environmental factors that plagued them from the first moment of their existence, and in the end must acknowledge that they were very far from living up to what had been expected of them.
We hear a lot about how "the generals" (that monolith!) resisted new technology out of some hidebound lack of imagination or fear that it wasn't somehow "proper." This is a greatly exaggerated thing to begin with, but in terms of tanks it's very far from the truth indeed. There was less reluctance about introducing the new weapon than there was regret that they could not introduce more of them and confusion over how to introduce them at all. They were damnably expensive to produce, slow to build, difficult to transport, and dramatically diminished in their power once the initial shock at their appearance had worn off. Still, many of their early proponents were almost fanatics on the subject; Winston Churchill, for example, in his capacity as Minister of Munitions in 1918, drafted a wildly hypothetical plan of attack that called for 10,000 tanks backed by an additional 8,000 to 10,000 tracked support vehicles (precursors to the APCs of the second war). This is a fantastic idea, or to be more precise fantastical; it ignores (as Churchill should have known then, but as he continued to ignore in his memoirs of the war published in the 1920s and 30s) the fact that no such manufacturing capacity existed, anywhere, to produce this number of tanks on the kind of timeframe that was envisioned.
We might look also to the ideas of Major General J.F.C. Fuller, who in the Spring of 1918 was inspired by the sight of British troops retreating near Peronne to imagine a future in which the tank made such a thing unnecessary. His idea ultimately became known as "Plan 1919", and we can find a fine description of its potential in A.J. Trythall's biography of Fuller:
[The basic concept] was derived from the question, 'Why were our troops retreating?' and the answer 'Because our command was paralysed.' The concept was 'strategic paralysis', to be brought about by attacking and cutting off the enemy's brains, in other words his field headquarters, from his fighting troops. 'Plan 1919' was originally called 'The Tactics of the Medium D Tank', but before becoming 'Plan 1919' became 'Strategical Paralysis as the Object of the Attack'. According to Fuller himself the idea was 'a psycho-tactical one', but he used 'strategical' rather than 'tactical' in conjunction with 'paralysis' because 'the primary aim of the attack was to paralyse the enemy's command and not his fighting forces... that is his strategical brain and not his fighting body.'
Fuller had based this plan on the imminent production of a then-still-hypothetical piece of weaponry, the Medium D tank. A single experimental model had been built in 1918 -- that was it. On paper it was absolutely wonderful by comparison to the rest of the tanks then available, but it only really existed on paper to begin with. This didn't stop Fuller from drafting a plan that would require 1,600 of the things, however, and an additional 400 smaller support tanks -- a plan that the course of events rendered moot, anyway, given that the war ended without it.
Those commanders who were able to make use of the tanks while the war was still in progress sent in similarly enormous purchase orders; Sir Douglas Haig, for example, had been absolutely convinced of the tank's importance even five months before any of them even arrived for his inspection, and only four days after their first action would place an order for another 1,000, to be delivered as quickly as possible.
The realities were almost dismal by comparison. There were 49 tanks available for their initial debut at Flers; only 32 of these actually reached the Front, with the rest being sidelined by a variety of mechanical and environmental problems. Further problems at the Front itself prevented all but 25 of the new vehicles from being deployed, and only 9 actually even made it to the German lines -- not an explosive start.
Still, they were an arguable success in their debut -- if we may call demonstrating dramatic potential without achieving much of it a success -- and one would think that Haig's enthusiastic request for a thousand of them would lead to increased production... but one would be wrong. By the opening of the Arras offensive six months later, only 60 were actually on hand, most of them actually having been refurbished from the action at Flers! By the height of Third Ypres this had only increased to 136. The opening of 1917 had seen the office initially in charge of tank production (the Heavy Branch of the Machine Gun Corps) make plans to produce 1,460 new tanks in the first nine months, including 1,000 of the Mark IVs and even, later in the year, some of the new Mark Vs. None of the latter ever did get produced that year, and of the former only 378 ever made it to the Battle of Cambrai in November -- where they were admittedly used to great effect.
None of this was made any easier by inter-departmental competition and basic design oversights, either. The Admiralty had been keeping a stranglehold on the supply of steel plate necessary for mass production of the tanks, and it was discovered belatedly that highly anticipated Mark IVs were being defeated in the field by the simple expedient of the Germans widening their trenches by two or three feet. This had been anticipated by the officers staffing the Tank HQ near the front lines, but none of the early recommendations they had made about improving the Mark IV's design had actually been accepted by its manufacturers, who felt they knew better.
The war's closing stages during the Battle of Amiens saw the deployment of a comparatively large number of tanks -- 342 Mark Vs and 72 Whippets. While they proved a potent force indeed, it would be worth considering their casualty rates:
Clearly there were still problems to be solved.
The main one was speed. Considerably behind the cavalry, armored cars and motorcycles of the time, the top speed of the 1918 Mark V on a smooth, open road was only 4.6 miles per hour. The same speed for the Medium Mark A Whippet was a more promising 8.3 miles per hour -- but, again, on a clear open road. Across the sort of crater-strewn, uneven terrain in which they would actually be deployed their usual speed was closer to 1-1.5 miles per hour -- hardly a replacement for cavalry when it came to swift maneuvers and immediate exploitation. They were also very poor as troop carriers; the great lumbering machines had serious ventilation problems that routinely left those riding in them in a state of near collapse after any sustained amount of time -- certainly in no condition for quick and dynamic action.
Worse still was the fact that, in spite of having been designed to repel small arms fire with impunity and traverse a variety of difficult terrains, there were still so many things that could just turn them into expensive wrecks at the drop of a hat. The things basically destroyed themselves; they were forever getting stuck in shell craters, or falling into trenches, or getting flipped over coming up or down hills, or simply breaking down in the middle of No Man's Land, stranding their crew in a very dangerous position indeed. Their armor was only barely "bullet-proof", and was in most cases wholly incapable of stopping the armor-piercing rounds developed to deal with them. Artillery was even worse; the gigantic, ponderous objects made amazing targets for gunners, and it was rare that more than a single well-aimed shell was needed to destroy one.
Sometimes this was taken to absurd extremes: the only German officer to have received the distinction of being mentioned in dispatches by Field Marshal Haig was the one who managed, while serving his gun single-handedly, to destroy sixteen British tanks one after another, each with a single shot. Haig notes this with a tone of frank admiration that was shared even by those on the scene, and it was a matter of some regret that the dedicated officer was finally killed at his gun.
I have no doubt that /u/elos_ may be along to add to all of this in his typically excellent manner, but this is what I've got for now.