Mechanization
As a result of the introduction of various forms of mechanized transport, starting with the steam powered trains in mid-19th century, logistics have been vastly improved and the opposing armies were no longer limited in speed by the pace of march. Some train-borne maneuvering took place during the American Civil War in the 1860s, but the sizes of the armies involved meant the system could provide only limited support. Armored trains were among the first armored fighting vehicles employed by mankind.
In the Franco-Prussian War the Prussian Army, knowing that they could field substantially larger forces than the French, devised a war plan that relied on speed by encircling and destroying/bypassing French strongpoints - the Kesselschlacht or "cauldron battle" - while the remainder of the Prussian army advanced unopposed to seize important objectives such as Paris.
If, on declaration of war, they could mobilize quickly, invade and destroy French field forces fast enough, then they would be victorious before the French army could react. This tactic was used to devastating effect in 1870, when the Prussian forces were able to rapidly encircle and defeat two large French forces before they were able to retreat.
Given the success they had in 1870s, it is not surprising that the German battle plan for the First World War would be similar. The Germans attempted to repeat the "knock-out blow" against the French armies in the Schlieffen Plan.
However technology had changed considerably in the four decades, with the machine gun and considerably more powerful artillery swinging the balance of power decisively to the defense. While all combatants were desperate to get the front moving again, this proved difficult.
The introduction of the tank in a series of increasingly successful operations pointed the way out of trench warfare, but the war ended before the British plans to field thousands of them could be put into place. Germany also introduced new tactics against static warfare with infiltration and stormtrooper tactics toward the end of World War I, which bypassed resistance leaving its reduction to other means. Russian general Aleksei Brusilov used similar tactics in 1916 on the Eastern front.
Between the World Wars the Germans again reviewed their doctrine and completely revised their approach again, perhaps getting back to some of the von Clausewitz ideas which were now enabled by motor transport. The integration of the main battle tank, with close air support, rapid movement of troops, and concentrated forces, were described as blitzkrieg, "Lightning War' by Heinz Guderian, who then deployed these tactics during Second World War. Blitzkrieg is perhaps the most famous example of maneuver warfare and derived in part from the theories of many, perhaps including British officer J.F.C. Fuller, of which the British army had failed to take advantage. Modern "Shock and Awe" tactics such as used by the US and Coalition forces in Desert Storm, are closely related to Blitzkrieg methods.
The Soviets used the concept of "Deep Battle" (which they continued through the Cold War). The Western Allies were strategically attrition-oriented, though there were many maneuver-minded commanders including O'Connor, Montgomery and Patton.
Read more about this topic: Maneuver Warfare